The replicator equation and other game dynamics

PubMed Central

Cressman, Ross; Tao, Yi

2014-01-01

The replicator equation is the first and most important game dynamics studied in connection with evolutionary game theory. It was originally developed for symmetric games with finitely many strategies. Properties of these dynamics are briefly summarized for this case, including the convergence to and stability of the Nash equilibria and evolutionarily stable strategies. The theory is then extended to other game dynamics for symmetric games (e.g., the best response dynamics and adaptive dynamics) and illustrated by examples taken from the literature. It is also extended to multiplayer, population, and asymmetric games. PMID:25024202

Bipartite Graphs as Models of Population Structures in Evolutionary Multiplayer Games

PubMed Central

Peña, Jorge; Rochat, Yannick

2012-01-01

By combining evolutionary game theory and graph theory, “games on graphs” study the evolutionary dynamics of frequency-dependent selection in population structures modeled as geographical or social networks. Networks are usually represented by means of unipartite graphs, and social interactions by two-person games such as the famous prisoner’s dilemma. Unipartite graphs have also been used for modeling interactions going beyond pairwise interactions. In this paper, we argue that bipartite graphs are a better alternative to unipartite graphs for describing population structures in evolutionary multiplayer games. To illustrate this point, we make use of bipartite graphs to investigate, by means of computer simulations, the evolution of cooperation under the conventional and the distributed N-person prisoner’s dilemma. We show that several implicit assumptions arising from the standard approach based on unipartite graphs (such as the definition of replacement neighborhoods, the intertwining of individual and group diversity, and the large overlap of interaction neighborhoods) can have a large impact on the resulting evolutionary dynamics. Our work provides a clear example of the importance of construction procedures in games on graphs, of the suitability of bigraphs and hypergraphs for computational modeling, and of the importance of concepts from social network analysis such as centrality, centralization and bipartite clustering for the understanding of dynamical processes occurring on networked population structures. PMID:22970237

Evolutionary Games with Randomly Changing Payoff Matrices

NASA Astrophysics Data System (ADS)

Yakushkina, Tatiana; Saakian, David B.; Bratus, Alexander; Hu, Chin-Kun

2015-06-01

Evolutionary games are used in various fields stretching from economics to biology. In most of these games a constant payoff matrix is assumed, although some works also consider dynamic payoff matrices. In this article we assume a possibility of switching the system between two regimes with different sets of payoff matrices. Potentially such a model can qualitatively describe the development of bacterial or cancer cells with a mutator gene present. A finite population evolutionary game is studied. The model describes the simplest version of annealed disorder in the payoff matrix and is exactly solvable at the large population limit. We analyze the dynamics of the model, and derive the equations for both the maximum and the variance of the distribution using the Hamilton-Jacobi equation formalism.

Effect of the spatial autocorrelation of empty sites on the evolution of cooperation

NASA Astrophysics Data System (ADS)

Zhang, Hui; Wang, Li; Hou, Dongshuang

2016-02-01

An evolutionary game model is constructed to investigate the spatial autocorrelation of empty sites on the evolution of cooperation. Each individual is assumed to imitate the strategy of the one who scores the highest in its neighborhood including itself. Simulation results illustrate that the evolutionary dynamics based on the Prisoner's Dilemma game (PD) depends severely on the initial conditions, while the Snowdrift game (SD) is hardly affected by that. A high degree of autocorrelation of empty sites is beneficial for the evolution of cooperation in the PD, whereas it shows diversification effects depending on the parameter of temptation to defect in the SD. Moreover, for the repeated game with three strategies, 'always defect' (ALLD), 'tit-for-tat' (TFT), and 'always cooperate' (ALLC), simulations reveal that an amazing evolutionary diversity appears for varying of parameters of the temptation to defect and the probability of playing in the next round of the game. The spatial autocorrelation of empty sites can have profound effects on evolutionary dynamics (equilibrium and oscillation) and spatial distribution.

The Price Equation, Gradient Dynamics, and Continuous Trait Game Theory.

PubMed

Lehtonen, Jussi

2018-01-01

A recent article convincingly nominated the Price equation as the fundamental theorem of evolution and used it as a foundation to derive several other theorems. A major section of evolutionary theory that was not addressed is that of game theory and gradient dynamics of continuous traits with frequency-dependent fitness. Deriving fundamental results in these fields under the unifying framework of the Price equation illuminates similarities and differences between approaches and allows a simple, unified view of game-theoretical and dynamic concepts. Using Taylor polynomials and the Price equation, I derive a dynamic measure of evolutionary change, a condition for singular points, the convergence stability criterion, and an alternative interpretation of evolutionary stability. Furthermore, by applying the Price equation to a multivariable Taylor polynomial, the direct fitness approach to kin selection emerges. Finally, I compare these results to the mean gradient equation of quantitative genetics and the canonical equation of adaptive dynamics.

Games of multicellularity.

PubMed

Kaveh, Kamran; Veller, Carl; Nowak, Martin A

2016-08-21

Evolutionary game dynamics are often studied in the context of different population structures. Here we propose a new population structure that is inspired by simple multicellular life forms. In our model, cells reproduce but can stay together after reproduction. They reach complexes of a certain size, n, before producing single cells again. The cells within a complex derive payoff from an evolutionary game by interacting with each other. The reproductive rate of cells is proportional to their payoff. We consider all two-strategy games. We study deterministic evolutionary dynamics with mutations, and derive exact conditions for selection to favor one strategy over another. Our main result has the same symmetry as the well-known sigma condition, which has been proven for stochastic game dynamics and weak selection. For a maximum complex size of n=2 our result holds for any intensity of selection. For n≥3 it holds for weak selection. As specific examples we study the prisoner's dilemma and hawk-dove games. Our model advances theoretical work on multicellularity by allowing for frequency-dependent interactions within groups. Copyright © 2016 Elsevier Ltd. All rights reserved.

Evolutionary Games in Multi-Agent Systems of Weighted Social Networks

NASA Astrophysics Data System (ADS)

Du, Wen-Bo; Cao, Xian-Bin; Zheng, Hao-Ran; Zhou, Hong; Hu, Mao-Bin

Much empirical evidence has shown realistic networks are weighted. Compared with those on unweighted networks, the dynamics on weighted network often exhibit distinctly different phenomena. In this paper, we investigate the evolutionary game dynamics (prisoner's dilemma game and snowdrift game) on a weighted social network consisted of rational agents and focus on the evolution of cooperation in the system. Simulation results show that the cooperation level is strongly affected by the weighted nature of the network. Moreover, the variation of time series has also been investigated. Our work may be helpful in understanding the cooperative behavior in the social systems.

Mean-Potential Law in Evolutionary Games

NASA Astrophysics Data System (ADS)

Nałecz-Jawecki, Paweł; Miekisz, Jacek

2018-01-01

The Letter presents a novel way to connect random walks, stochastic differential equations, and evolutionary game theory. We introduce a new concept of a potential function for discrete-space stochastic systems. It is based on a correspondence between one-dimensional stochastic differential equations and random walks, which may be exact not only in the continuous limit but also in finite-state spaces. Our method is useful for computation of fixation probabilities in discrete stochastic dynamical systems with two absorbing states. We apply it to evolutionary games, formulating two simple and intuitive criteria for evolutionary stability of pure Nash equilibria in finite populations. In particular, we show that the 1 /3 law of evolutionary games, introduced by Nowak et al. [Nature, 2004], follows from a more general mean-potential law.

On the preservation of cooperation in two-strategy games with nonlocal interactions.

PubMed

Aydogmus, Ozgur; Zhou, Wen; Kang, Yun

2017-03-01

Nonlocal interactions such as spatial interaction are ubiquitous in nature and may alter the equilibrium in evolutionary dynamics. Models including nonlocal spatial interactions can provide a further understanding on the preservation and emergence of cooperation in evolutionary dynamics. In this paper, we consider a variety of two-strategy evolutionary spatial games with nonlocal interactions based on an integro-differential replicator equation. By defining the invasion speed and minimal traveling wave speed for the derived model, we study the effects of the payoffs, the selection pressure and the spatial parameter on the preservation of cooperation. One of our most interesting findings is that, for the Prisoners Dilemma games in which the defection is the only evolutionary stable strategy for unstructured populations, analyses on its asymptotic speed of propagation suggest that, in contrast with spatially homogeneous games, the cooperators can invade the habitat under proper conditions. Other two-strategy evolutionary spatial games are also explored. Both our theoretical and numerical studies show that the nonlocal spatial interaction favors diversity in strategies in a population and is able to preserve cooperation in a competing environment. A real data application in a virus mutation study echoes our theoretical observations. In addition, we compare the results of our model to the partial differential equation approach to demonstrate the importance of including non-local interaction component in evolutionary game models. Copyright © 2016 Elsevier Inc. All rights reserved.

Public goods games in populations with fluctuating size.

PubMed

McAvoy, Alex; Fraiman, Nicolas; Hauert, Christoph; Wakeley, John; Nowak, Martin A

2018-05-01

Many mathematical frameworks of evolutionary game dynamics assume that the total population size is constant and that selection affects only the relative frequency of strategies. Here, we consider evolutionary game dynamics in an extended Wright-Fisher process with variable population size. In such a scenario, it is possible that the entire population becomes extinct. Survival of the population may depend on which strategy prevails in the game dynamics. Studying cooperative dilemmas, it is a natural feature of such a model that cooperators enable survival, while defectors drive extinction. Although defectors are favored for any mixed population, random drift could lead to their elimination and the resulting pure-cooperator population could survive. On the other hand, if the defectors remain, then the population will quickly go extinct because the frequency of cooperators steadily declines and defectors alone cannot survive. In a mutation-selection model, we find that (i) a steady supply of cooperators can enable long-term population survival, provided selection is sufficiently strong, and (ii) selection can increase the abundance of cooperators but reduce their relative frequency. Thus, evolutionary game dynamics in populations with variable size generate a multifaceted notion of what constitutes a trait's long-term success. Copyright © 2018 Elsevier Inc. All rights reserved.

Unfair and Anomalous Evolutionary Dynamics from Fluctuating Payoffs.

PubMed

Stollmeier, Frank; Nagler, Jan

2018-02-02

Evolution occurs in populations of reproducing individuals. Reproduction depends on the payoff a strategy receives. The payoff depends on the environment that may change over time, on intrinsic uncertainties, and on other sources of randomness. These temporal variations in the payoffs can affect which traits evolve. Understanding evolutionary game dynamics that are affected by varying payoffs remains difficult. Here we study the impact of arbitrary amplitudes and covariances of temporally varying payoffs on the dynamics. The evolutionary dynamics may be "unfair," meaning that, on average, two coexisting strategies may persistently receive different payoffs. This mechanism can induce an anomalous coexistence of cooperators and defectors in the prisoner's dilemma, and an unexpected selection reversal in the hawk-dove game.

Unfair and Anomalous Evolutionary Dynamics from Fluctuating Payoffs

NASA Astrophysics Data System (ADS)

Stollmeier, Frank; Nagler, Jan

2018-02-01

Evolution occurs in populations of reproducing individuals. Reproduction depends on the payoff a strategy receives. The payoff depends on the environment that may change over time, on intrinsic uncertainties, and on other sources of randomness. These temporal variations in the payoffs can affect which traits evolve. Understanding evolutionary game dynamics that are affected by varying payoffs remains difficult. Here we study the impact of arbitrary amplitudes and covariances of temporally varying payoffs on the dynamics. The evolutionary dynamics may be "unfair," meaning that, on average, two coexisting strategies may persistently receive different payoffs. This mechanism can induce an anomalous coexistence of cooperators and defectors in the prisoner's dilemma, and an unexpected selection reversal in the hawk-dove game.

Research on Information Sharing Mechanism of Network Organization Based on Evolutionary Game

NASA Astrophysics Data System (ADS)

Wang, Lin; Liu, Gaozhi

2018-02-01

This article first elaborates the concept and effect of network organization, and the ability to share information is analyzed, secondly introduces the evolutionary game theory, network organization for information sharing all kinds of limitations, establishes the evolutionary game model, analyzes the dynamic evolution of network organization of information sharing, through reasoning and evolution. The network information sharing by the initial state and two sides of the game payoff matrix of excess profits and information is the information sharing of cost and risk sharing are the influence of network organization node information sharing decision.

Cooperation in two-person evolutionary games with complex personality profiles.

PubMed

Płatkowski, Tadeusz

2010-10-21

We propose a theory of evolution of social systems which generalizes the standard proportional fitness rule of the evolutionary game theory. The formalism is applied to describe the dynamics of two-person one-shot population games. In particular it predicts the non-zero level of cooperation in the long run for the Prisoner's Dilemma games, the increase of the fraction of cooperators for general classes of the Snow-Drift game, and stable nonzero cooperation level for coordination games. Copyright © 2010 Elsevier Ltd. All rights reserved.

Mean-Potential Law in Evolutionary Games.

PubMed

Nałęcz-Jawecki, Paweł; Miękisz, Jacek

2018-01-12

The Letter presents a novel way to connect random walks, stochastic differential equations, and evolutionary game theory. We introduce a new concept of a potential function for discrete-space stochastic systems. It is based on a correspondence between one-dimensional stochastic differential equations and random walks, which may be exact not only in the continuous limit but also in finite-state spaces. Our method is useful for computation of fixation probabilities in discrete stochastic dynamical systems with two absorbing states. We apply it to evolutionary games, formulating two simple and intuitive criteria for evolutionary stability of pure Nash equilibria in finite populations. In particular, we show that the 1/3 law of evolutionary games, introduced by Nowak et al. [Nature, 2004], follows from a more general mean-potential law.

Stochastic noncooperative and cooperative evolutionary game strategies of a population of biological networks under natural selection.

PubMed

Chen, Bor-Sen; Yeh, Chin-Hsun

2017-12-01

We review current static and dynamic evolutionary game strategies of biological networks and discuss the lack of random genetic variations and stochastic environmental disturbances in these models. To include these factors, a population of evolving biological networks is modeled as a nonlinear stochastic biological system with Poisson-driven genetic variations and random environmental fluctuations (stimuli). To gain insight into the evolutionary game theory of stochastic biological networks under natural selection, the phenotypic robustness and network evolvability of noncooperative and cooperative evolutionary game strategies are discussed from a stochastic Nash game perspective. The noncooperative strategy can be transformed into an equivalent multi-objective optimization problem and is shown to display significantly improved network robustness to tolerate genetic variations and buffer environmental disturbances, maintaining phenotypic traits for longer than the cooperative strategy. However, the noncooperative case requires greater effort and more compromises between partly conflicting players. Global linearization is used to simplify the problem of solving nonlinear stochastic evolutionary games. Finally, a simple stochastic evolutionary model of a metabolic pathway is simulated to illustrate the procedure of solving for two evolutionary game strategies and to confirm and compare their respective characteristics in the evolutionary process. Copyright © 2017 Elsevier B.V. All rights reserved.

Strategy selection in structured populations.

PubMed

Tarnita, Corina E; Ohtsuki, Hisashi; Antal, Tibor; Fu, Feng; Nowak, Martin A

2009-08-07

Evolutionary game theory studies frequency dependent selection. The fitness of a strategy is not constant, but depends on the relative frequencies of strategies in the population. This type of evolutionary dynamics occurs in many settings of ecology, infectious disease dynamics, animal behavior and social interactions of humans. Traditionally evolutionary game dynamics are studied in well-mixed populations, where the interaction between any two individuals is equally likely. There have also been several approaches to study evolutionary games in structured populations. In this paper we present a simple result that holds for a large variety of population structures. We consider the game between two strategies, A and B, described by the payoff matrix(abcd). We study a mutation and selection process. For weak selection strategy A is favored over B if and only if sigma a+b>c+sigma d. This means the effect of population structure on strategy selection can be described by a single parameter, sigma. We present the values of sigma for various examples including the well-mixed population, games on graphs, games in phenotype space and games on sets. We give a proof for the existence of such a sigma, which holds for all population structures and update rules that have certain (natural) properties. We assume weak selection, but allow any mutation rate. We discuss the relationship between sigma and the critical benefit to cost ratio for the evolution of cooperation. The single parameter, sigma, allows us to quantify the ability of a population structure to promote the evolution of cooperation or to choose efficient equilibria in coordination games.

The Stochastic Evolutionary Game for a Population of Biological Networks Under Natural Selection

PubMed Central

Chen, Bor-Sen; Ho, Shih-Ju

2014-01-01

In this study, a population of evolutionary biological networks is described by a stochastic dynamic system with intrinsic random parameter fluctuations due to genetic variations and external disturbances caused by environmental changes in the evolutionary process. Since information on environmental changes is unavailable and their occurrence is unpredictable, they can be considered as a game player with the potential to destroy phenotypic stability. The biological network needs to develop an evolutionary strategy to improve phenotypic stability as much as possible, so it can be considered as another game player in the evolutionary process, ie, a stochastic Nash game of minimizing the maximum network evolution level caused by the worst environmental disturbances. Based on the nonlinear stochastic evolutionary game strategy, we find that some genetic variations can be used in natural selection to construct negative feedback loops, efficiently improving network robustness. This provides larger genetic robustness as a buffer against neutral genetic variations, as well as larger environmental robustness to resist environmental disturbances and maintain a network phenotypic traits in the evolutionary process. In this situation, the robust phenotypic traits of stochastic biological networks can be more frequently selected by natural selection in evolution. However, if the harbored neutral genetic variations are accumulated to a sufficiently large degree, and environmental disturbances are strong enough that the network robustness can no longer confer enough genetic robustness and environmental robustness, then the phenotype robustness might break down. In this case, a network phenotypic trait may be pushed from one equilibrium point to another, changing the phenotypic trait and starting a new phase of network evolution through the hidden neutral genetic variations harbored in network robustness by adaptive evolution. Further, the proposed evolutionary game is extended to an n-tuple evolutionary game of stochastic biological networks with m players (competitive populations) and k environmental dynamics. PMID:24558296

Mean-field approximations of fixation time distributions of evolutionary game dynamics on graphs

NASA Astrophysics Data System (ADS)

Ying, Li-Min; Zhou, Jie; Tang, Ming; Guan, Shu-Guang; Zou, Yong

2018-02-01

The mean fixation time is often not accurate for describing the timescales of fixation probabilities of evolutionary games taking place on complex networks. We simulate the game dynamics on top of complex network topologies and approximate the fixation time distributions using a mean-field approach. We assume that there are two absorbing states. Numerically, we show that the mean fixation time is sufficient in characterizing the evolutionary timescales when network structures are close to the well-mixing condition. In contrast, the mean fixation time shows large inaccuracies when networks become sparse. The approximation accuracy is determined by the network structure, and hence by the suitability of the mean-field approach. The numerical results show good agreement with the theoretical predictions.

Evolutionary games in the multiverse.

PubMed

Gokhale, Chaitanya S; Traulsen, Arne

2010-03-23

Evolutionary game dynamics of two players with two strategies has been studied in great detail. These games have been used to model many biologically relevant scenarios, ranging from social dilemmas in mammals to microbial diversity. Some of these games may, in fact, take place between a number of individuals and not just between two. Here we address one-shot games with multiple players. As long as we have only two strategies, many results from two-player games can be generalized to multiple players. For games with multiple players and more than two strategies, we show that statements derived for pairwise interactions no longer hold. For two-player games with any number of strategies there can be at most one isolated internal equilibrium. For any number of players with any number of strategies , there can be at most isolated internal equilibria. Multiplayer games show a great dynamical complexity that cannot be captured based on pairwise interactions. Our results hold for any game and can easily be applied to specific cases, such as public goods games or multiplayer stag hunts.

Evolutionary dynamics on graphs: Efficient method for weak selection

NASA Astrophysics Data System (ADS)

Fu, Feng; Wang, Long; Nowak, Martin A.; Hauert, Christoph

2009-04-01

Investigating the evolutionary dynamics of game theoretical interactions in populations where individuals are arranged on a graph can be challenging in terms of computation time. Here, we propose an efficient method to study any type of game on arbitrary graph structures for weak selection. In this limit, evolutionary game dynamics represents a first-order correction to neutral evolution. Spatial correlations can be empirically determined under neutral evolution and provide the basis for formulating the game dynamics as a discrete Markov process by incorporating a detailed description of the microscopic dynamics based on the neutral correlations. This framework is then applied to one of the most intriguing questions in evolutionary biology: the evolution of cooperation. We demonstrate that the degree heterogeneity of a graph impedes cooperation and that the success of tit for tat depends not only on the number of rounds but also on the degree of the graph. Moreover, considering the mutation-selection equilibrium shows that the symmetry of the stationary distribution of states under weak selection is skewed in favor of defectors for larger selection strengths. In particular, degree heterogeneity—a prominent feature of scale-free networks—generally results in a more pronounced increase in the critical benefit-to-cost ratio required for evolution to favor cooperation as compared to regular graphs. This conclusion is corroborated by an analysis of the effects of population structures on the fixation probabilities of strategies in general 2×2 games for different types of graphs. Computer simulations confirm the predictive power of our method and illustrate the improved accuracy as compared to previous studies.

Topological enslavement in evolutionary games on correlated multiplex networks

NASA Astrophysics Data System (ADS)

Kleineberg, Kaj-Kolja; Helbing, Dirk

2018-05-01

Governments and enterprises strongly rely on incentives to generate favorable outcomes from social and strategic interactions between individuals. The incentives are usually modeled by payoffs in evolutionary games, such as the prisoners dilemma or the harmony game, with imitation dynamics. Adjusting the incentives by changing the payoff parameters can favor cooperation, as found in the harmony game, over defection, which prevails in the prisoner’s dilemma. Here, we show that this is not always the case if individuals engage in strategic interactions in multiple domains. In particular, we investigate evolutionary games on multiplex networks where individuals obtain an aggregate payoff. We explicitly control the strength of degree correlations between nodes in the different layers of the multiplex. We find that if the multiplex is composed of many layers and degree correlations are strong, the topology of the system enslaves the dynamics and the final outcome, cooperation or defection, becomes independent of the payoff parameters. The fate of the system is then determined by the initial conditions.

Promotion of cooperation in evolutionary game dynamics with local information.

PubMed

Liu, Xuesong; Pan, Qiuhui; He, Mingfeng

2018-01-21

In this paper, we propose a strategy-updating rule driven by local information, which is called Local process. Unlike the standard Moran process, the Local process does not require global information about the strategic environment. By analyzing the dynamical behavior of the system, we explore how the local information influences the fixation of cooperation in two-player evolutionary games. Under weak selection, the decreasing local information leads to an increase of the fixation probability when natural selection does not favor cooperation replacing defection. In the limit of sufficiently large selection, the analytical results indicate that the fixation probability increases with the decrease of the local information, irrespective of the evolutionary games. Furthermore, for the dominance of defection games under weak selection and for coexistence games, the decreasing of local information will lead to a speedup of a single cooperator taking over the population. Overall, to some extent, the local information is conducive to promoting the cooperation. Copyright © 2017 Elsevier Ltd. All rights reserved.

Importance of tie strengths in the prisoner's dilemma game on social networks

NASA Astrophysics Data System (ADS)

Xu, Bo; Liu, Lu; You, Weijia

2011-06-01

Though numerous researches have shown that tie strengths play a key role in the formation of collective behavior in social networks, little work has been done to explore their impact on the outcome of evolutionary games. In this Letter, we studied the effect of tie strength in the dynamics of evolutionary prisoner's dilemma games by using online social network datasets. The results show that the fraction of cooperators has a non-trivial dependence on tie strength. Weak ties, just like previous researches on epidemics and information diffusion have shown, play a key role by the maintenance of cooperators in evolutionary prisoner's dilemma games.

Evolutionary game theory for physical and biological scientists. I. Training and validating population dynamics equations.

PubMed

Liao, David; Tlsty, Thea D

2014-08-06

Failure to understand evolutionary dynamics has been hypothesized as limiting our ability to control biological systems. An increasing awareness of similarities between macroscopic ecosystems and cellular tissues has inspired optimism that game theory will provide insights into the progression and control of cancer. To realize this potential, the ability to compare game theoretic models and experimental measurements of population dynamics should be broadly disseminated. In this tutorial, we present an analysis method that can be used to train parameters in game theoretic dynamics equations, used to validate the resulting equations, and used to make predictions to challenge these equations and to design treatment strategies. The data analysis techniques in this tutorial are adapted from the analysis of reaction kinetics using the method of initial rates taught in undergraduate general chemistry courses. Reliance on computer programming is avoided to encourage the adoption of these methods as routine bench activities.

Spatial pattern dynamics due to the fitness gradient flux in evolutionary games.

PubMed

deForest, Russ; Belmonte, Andrew

2013-06-01

We introduce a nondiffusive spatial coupling term into the replicator equation of evolutionary game theory. The spatial flux is based on motion due to local gradients in the relative fitness of each strategy, providing a game-dependent alternative to diffusive coupling. We study numerically the development of patterns in one dimension (1D) for two-strategy games including the coordination game and the prisoner's dilemma, and in two dimensions (2D) for the rock-paper-scissors game. In 1D we observe modified traveling wave solutions in the presence of diffusion, and asymptotic attracting states under a frozen-strategy assumption without diffusion. In 2D we observe spiral formation and breakup in the frozen-strategy rock-paper-scissors game without diffusion. A change of variables appropriate to replicator dynamics is shown to correctly capture the 1D asymptotic steady state via a nonlinear diffusion equation.

Spatial pattern dynamics due to the fitness gradient flux in evolutionary games

NASA Astrophysics Data System (ADS)

deForest, Russ; Belmonte, Andrew

2013-06-01

We introduce a nondiffusive spatial coupling term into the replicator equation of evolutionary game theory. The spatial flux is based on motion due to local gradients in the relative fitness of each strategy, providing a game-dependent alternative to diffusive coupling. We study numerically the development of patterns in one dimension (1D) for two-strategy games including the coordination game and the prisoner's dilemma, and in two dimensions (2D) for the rock-paper-scissors game. In 1D we observe modified traveling wave solutions in the presence of diffusion, and asymptotic attracting states under a frozen-strategy assumption without diffusion. In 2D we observe spiral formation and breakup in the frozen-strategy rock-paper-scissors game without diffusion. A change of variables appropriate to replicator dynamics is shown to correctly capture the 1D asymptotic steady state via a nonlinear diffusion equation.

Evolutionary dynamics of public goods games with diverse contributions in finite populations

NASA Astrophysics Data System (ADS)

Wang, Jing; Wu, Bin; Chen, Xiaojie; Wang, Long

2010-05-01

The public goods game is a powerful metaphor for exploring the maintenance of social cooperative behavior in a group of interactional selfish players. Here we study the emergence of cooperation in the public goods games with diverse contributions in finite populations. The theory of stochastic process is innovatively adopted to investigate the evolutionary dynamics of the public goods games involving a diversity of contributions. In the limit of rare mutations, the general stationary distribution of this stochastic process can be analytically approximated by means of diffusion theory. Moreover, we demonstrate that increasing the diversity of contributions greatly reduces the probability of finding the population in a homogeneous state full of defectors. This increase also raises the expectation of the total contribution in the entire population and thus promotes social cooperation. Furthermore, by investigating the evolutionary dynamics of optional public goods games with diverse contributions, we find that nonparticipation can assist players who contribute more in resisting invasion and taking over individuals who contribute less. In addition, numerical simulations are performed to confirm our analytical results. Our results may provide insight into the effect of diverse contributions on cooperative behaviors in the real world.

Darwinism in quantum systems?

NASA Astrophysics Data System (ADS)

Iqbal, A.; Toor, A. H.

2002-03-01

We investigate the role of quantum mechanical effects in the central stability concept of evolutionary game theory, i.e., an evolutionarily stable strategy (ESS). Using two and three-player symmetric quantum games we show how the presence of quantum phenomenon of entanglement can be crucial to decide the course of evolutionary dynamics in a population of interacting individuals.

Analytical model for minority games with evolutionary learning

NASA Astrophysics Data System (ADS)

Campos, Daniel; Méndez, Vicenç; Llebot, Josep E.; Hernández, Germán A.

2010-06-01

In a recent work [D. Campos, J.E. Llebot, V. Méndez, Theor. Popul. Biol. 74 (2009) 16] we have introduced a biological version of the Evolutionary Minority Game that tries to reproduce the intraspecific competition for limited resources in an ecosystem. In comparison with the complex decision-making mechanisms used in standard Minority Games, only two extremely simple strategies ( juveniles and adults) are accessible to the agents. Complexity is introduced instead through an evolutionary learning rule that allows younger agents to learn taking better decisions. We find that this game shows many of the typical properties found for Evolutionary Minority Games, like self-segregation behavior or the existence of an oscillation phase for a certain range of the parameter values. However, an analytical treatment becomes much easier in our case, taking advantage of the simple strategies considered. Using a model consisting of a simple dynamical system, the phase diagram of the game (which differentiates three phases: adults crowd, juveniles crowd and oscillations) is reproduced.

Co-Evolution of Opinion and Strategy in Persuasion Dynamics:. AN Evolutionary Game Theoretical Approach

NASA Astrophysics Data System (ADS)

Ding, Fei; Liu, Yun; Li, Yong

In this paper, a new model of opinion formation within the framework of evolutionary game theory is presented. The model simulates strategic situations when people are in opinion discussion. Heterogeneous agents adjust their behaviors to the environment during discussions, and their interacting strategies evolve together with opinions. In the proposed game, we take into account payoff discount to join a discussion, and the situation that people might drop out of an unpromising game. Analytical and emulational results show that evolution of opinion and strategy always tend to converge, with utility threshold, memory length, and decision uncertainty parameters influencing the convergence time. The model displays different dynamical regimes when we set differently the rule when people are at a loss in strategy.

Multiscale structure in eco-evolutionary dynamics

NASA Astrophysics Data System (ADS)

Stacey, Blake C.

In a complex system, the individual components are neither so tightly coupled or correlated that they can all be treated as a single unit, nor so uncorrelated that they can be approximated as independent entities. Instead, patterns of interdependency lead to structure at multiple scales of organization. Evolution excels at producing such complex structures. In turn, the existence of these complex interrelationships within a biological system affects the evolutionary dynamics of that system. I present a mathematical formalism for multiscale structure, grounded in information theory, which makes these intuitions quantitative, and I show how dynamics defined in terms of population genetics or evolutionary game theory can lead to multiscale organization. For complex systems, "more is different," and I address this from several perspectives. Spatial host--consumer models demonstrate the importance of the structures which can arise due to dynamical pattern formation. Evolutionary game theory reveals the novel effects which can result from multiplayer games, nonlinear payoffs and ecological stochasticity. Replicator dynamics in an environment with mesoscale structure relates to generalized conditionalization rules in probability theory. The idea of natural selection "acting at multiple levels" has been mathematized in a variety of ways, not all of which are equivalent. We will face down the confusion, using the experience developed over the course of this thesis to clarify the situation.

Evolutionary games in the multiverse

PubMed Central

Gokhale, Chaitanya S.; Traulsen, Arne

2010-01-01

Evolutionary game dynamics of two players with two strategies has been studied in great detail. These games have been used to model many biologically relevant scenarios, ranging from social dilemmas in mammals to microbial diversity. Some of these games may, in fact, take place between a number of individuals and not just between two. Here we address one-shot games with multiple players. As long as we have only two strategies, many results from two-player games can be generalized to multiple players. For games with multiple players and more than two strategies, we show that statements derived for pairwise interactions no longer hold. For two-player games with any number of strategies there can be at most one isolated internal equilibrium. For any number of players with any number of strategies , there can be at most isolated internal equilibria. Multiplayer games show a great dynamical complexity that cannot be captured based on pairwise interactions. Our results hold for any game and can easily be applied to specific cases, such as public goods games or multiplayer stag hunts. PMID:20212124

Stability of Mixed-Strategy-Based Iterative Logit Quantal Response Dynamics in Game Theory

PubMed Central

Zhuang, Qian; Di, Zengru; Wu, Jinshan

2014-01-01

Using the Logit quantal response form as the response function in each step, the original definition of static quantal response equilibrium (QRE) is extended into an iterative evolution process. QREs remain as the fixed points of the dynamic process. However, depending on whether such fixed points are the long-term solutions of the dynamic process, they can be classified into stable (SQREs) and unstable (USQREs) equilibriums. This extension resembles the extension from static Nash equilibriums (NEs) to evolutionary stable solutions in the framework of evolutionary game theory. The relation between SQREs and other solution concepts of games, including NEs and QREs, is discussed. Using experimental data from other published papers, we perform a preliminary comparison between SQREs, NEs, QREs and the observed behavioral outcomes of those experiments. For certain games, we determine that SQREs have better predictive power than QREs and NEs. PMID:25157502

Stochastic dynamics and stable equilibrium of evolutionary optional public goods game in finite populations

NASA Astrophysics Data System (ADS)

Quan, Ji; Liu, Wei; Chu, Yuqing; Wang, Xianjia

2018-07-01

Continuous noise caused by mutation is widely present in evolutionary systems. Considering the noise effects and under the optional participation mechanism, a stochastic model for evolutionary public goods game in a finite size population is established. The evolutionary process of strategies in the population is described as a multidimensional ergodic and continuous time Markov process. The stochastic stable state of the system is analyzed by the limit distribution of the stochastic process. By numerical experiments, the influences of the fixed income coefficient for non-participants and the investment income coefficient of the public goods on the stochastic stable equilibrium of the system are analyzed. Through the numerical calculation results, we found that the optional participation mechanism can change the evolutionary dynamics and the equilibrium of the public goods game, and there is a range of parameters which can effectively promote the evolution of cooperation. Further, we obtain the accurate quantitative relationship between the parameters and the probabilities for the system to choose different stable equilibriums, which can be used to realize the control of cooperation.

Dynamics in atomic signaling games.

PubMed

Fox, Michael J; Touri, Behrouz; Shamma, Jeff S

2015-07-07

We study an atomic signaling game under stochastic evolutionary dynamics. There are a finite number of players who repeatedly update from a finite number of available languages/signaling strategies. Players imitate the most fit agents with high probability or mutate with low probability. We analyze the long-run distribution of states and show that, for sufficiently small mutation probability, its support is limited to efficient communication systems. We find that this behavior is insensitive to the particular choice of evolutionary dynamic, a property that is due to the game having a potential structure with a potential function corresponding to average fitness. Consequently, the model supports conclusions similar to those found in the literature on language competition. That is, we show that efficient languages eventually predominate the society while reproducing the empirical phenomenon of linguistic drift. The emergence of efficiency in the atomic case can be contrasted with results for non-atomic signaling games that establish the non-negligible possibility of convergence, under replicator dynamics, to states of unbounded efficiency loss. Copyright © 2015 Elsevier Ltd. All rights reserved.

The one-third law of evolutionary dynamics.

PubMed

Ohtsuki, Hisashi; Bordalo, Pedro; Nowak, Martin A

2007-11-21

Evolutionary game dynamics in finite populations provide a new framework for studying selection of traits with frequency-dependent fitness. Recently, a "one-third law" of evolutionary dynamics has been described, which states that strategy A fixates in a B-population with selective advantage if the fitness of A is greater than that of B when A has a frequency 13. This relationship holds for all evolutionary processes examined so far, from the Moran process to games on graphs. However, the origin of the "number"13 is not understood. In this paper we provide an intuitive explanation by studying the underlying stochastic processes. We find that in one invasion attempt, an individual interacts on average with B-players twice as often as with A-players, which yields the one-third law. We also show that the one-third law implies that the average Malthusian fitness of A is positive.

Fixation, transient landscape, and diffusion dilemma in stochastic evolutionary game dynamics

NASA Astrophysics Data System (ADS)

Zhou, Da; Qian, Hong

2011-09-01

Agent-based stochastic models for finite populations have recently received much attention in the game theory of evolutionary dynamics. Both the ultimate fixation and the pre-fixation transient behavior are important to a full understanding of the dynamics. In this paper, we study the transient dynamics of the well-mixed Moran process through constructing a landscape function. It is shown that the landscape playing a central theoretical “device” that integrates several lines of inquiries: the stable behavior of the replicator dynamics, the long-time fixation, and continuous diffusion approximation associated with asymptotically large population. Several issues relating to the transient dynamics are discussed: (i) multiple time scales phenomenon associated with intra- and inter-attractoral dynamics; (ii) discontinuous transition in stochastically stationary process akin to Maxwell construction in equilibrium statistical physics; and (iii) the dilemma diffusion approximation facing as a continuous approximation of the discrete evolutionary dynamics. It is found that rare events with exponentially small probabilities, corresponding to the uphill movements and barrier crossing in the landscape with multiple wells that are made possible by strong nonlinear dynamics, plays an important role in understanding the origin of the complexity in evolutionary, nonlinear biological systems.

Evolutionary games under incompetence.

PubMed

Kleshnina, Maria; Filar, Jerzy A; Ejov, Vladimir; McKerral, Jody C

2018-02-26

The adaptation process of a species to a new environment is a significant area of study in biology. As part of natural selection, adaptation is a mutation process which improves survival skills and reproductive functions of species. Here, we investigate this process by combining the idea of incompetence with evolutionary game theory. In the sense of evolution, incompetence and training can be interpreted as a special learning process. With focus on the social side of the problem, we analyze the influence of incompetence on behavior of species. We introduce an incompetence parameter into a learning function in a single-population game and analyze its effect on the outcome of the replicator dynamics. Incompetence can change the outcome of the game and its dynamics, indicating its significance within what are inherently imperfect natural systems.

Stochastic evolutionary dynamics in minimum-effort coordination games

NASA Astrophysics Data System (ADS)

Li, Kun; Cong, Rui; Wang, Long

2016-08-01

The minimum-effort coordination game draws recently more attention for the fact that human behavior in this social dilemma is often inconsistent with the predictions of classical game theory. Here, we combine evolutionary game theory and coalescence theory to investigate this game in finite populations. Both analytic results and individual-based simulations show that effort costs play a key role in the evolution of contribution levels, which is in good agreement with those observed experimentally. Besides well-mixed populations, set structured populations have also been taken into consideration. Therein we find that large number of sets and moderate migration rate greatly promote effort levels, especially for high effort costs.

Evolutionary games on graphs

NASA Astrophysics Data System (ADS)

Szabó, György; Fáth, Gábor

2007-07-01

Game theory is one of the key paradigms behind many scientific disciplines from biology to behavioral sciences to economics. In its evolutionary form and especially when the interacting agents are linked in a specific social network the underlying solution concepts and methods are very similar to those applied in non-equilibrium statistical physics. This review gives a tutorial-type overview of the field for physicists. The first four sections introduce the necessary background in classical and evolutionary game theory from the basic definitions to the most important results. The fifth section surveys the topological complications implied by non-mean-field-type social network structures in general. The next three sections discuss in detail the dynamic behavior of three prominent classes of models: the Prisoner's Dilemma, the Rock-Scissors-Paper game, and Competing Associations. The major theme of the review is in what sense and how the graph structure of interactions can modify and enrich the picture of long term behavioral patterns emerging in evolutionary games.

How mutation affects evolutionary games on graphs

PubMed Central

Allen, Benjamin; Traulsen, Arne; Tarnita, Corina E.; Nowak, Martin A.

2011-01-01

Evolutionary dynamics are affected by population structure, mutation rates and update rules. Spatial or network structure facilitates the clustering of strategies, which represents a mechanism for the evolution of cooperation. Mutation dilutes this effect. Here we analyze how mutation influences evolutionary clustering on graphs. We introduce new mathematical methods to evolutionary game theory, specifically the analysis of coalescing random walks via generating functions. These techniques allow us to derive exact identity-by-descent (IBD) probabilities, which characterize spatial assortment on lattices and Cayley trees. From these IBD probabilities we obtain exact conditions for the evolution of cooperation and other game strategies, showing the dual effects of graph topology and mutation rate. High mutation rates diminish the clustering of cooperators, hindering their evolutionary success. Our model can represent either genetic evolution with mutation, or social imitation processes with random strategy exploration. PMID:21473871

Evolutionary dynamics in finite populations can explain the full range of cooperative behaviors observed in the centipede game.

PubMed

Rand, David G; Nowak, Martin A

2012-05-07

Classical economic models make behavioral predictions based on the assumption that people are fully rational and care only about maximizing their own payoffs. Although this approach successfully explains human behavior in many situations, there is a wealth of experimental evidence demonstrating conditions where people deviate from the predictions of these models. One setting that has received particular attention is fixed length repeated games. Iterating a social dilemma can promote cooperation through direct reciprocity, even if it is common knowledge that all players are rational and self-interested. However, this is not the case if the length of the game is known to the players. In the final round, a rational player will defect, because there is no future to be concerned with. But if you know the other player will defect in the last round, then you should defect in the second to last round, and so on. This logic of backwards induction leads to immediate defection as the only rational (sub-game perfect Nash equilibrium) strategy. When people actually play such games, however, immediate defection is rare. Here we use evolutionary dynamics in finite populations to study the centipede game, which is designed to explore this issue of backwards induction. We make the following observation: since full cooperation can risk-dominate immediate defection in the centipede game, stochastic evolutionary dynamics can favor both delayed defection and even full cooperation. Furthermore, our evolutionary model can quantitatively reproduce human behavior from two experiments by fitting a single free parameter, which is the product of population size and selection intensity. Thus we provide evidence that people's cooperative behavior in fixed length games, which is often called 'irrational', may in fact be the favored outcome of natural selection. Copyright © 2012 Elsevier Ltd. All rights reserved.

Stability of Zero-Sum Games in Evolutionary Game Theory

NASA Astrophysics Data System (ADS)

Knebel, Johannes; Krueger, Torben; Weber, Markus F.; Frey, Erwin

2014-03-01

Evolutionary game theory has evolved into a successful theoretical concept to study mechanisms that govern the evolution of ecological communities. On a mathematical level, this theory was formalized in the framework of the celebrated replicator equations (REs) and its stochastic generalizations. In our work, we analyze the long-time behavior of the REs for zero-sum games with arbitrarily many strategies, which are generalized versions of the children's game Rock-Paper-Scissors.[1] We demonstrate how to determine the strategies that survive and those that become extinct in the long run. Our results show that extinction of strategies is exponentially fast in generic setups, and that conditions for the survival can be formulated in terms of the Pfaffian of the REs' antisymmetric payoff matrix. Consequences for the stochastic dynamics, which arise in finite populations, are reflected by a generalized scaling law for the extinction time in the vicinity of critical reaction rates. Our findings underline the relevance of zero-sum games as a reference for the analysis of other models in evolutionary game theory.

Reciprocity in spatial evolutionary public goods game on double-layered network

NASA Astrophysics Data System (ADS)

Kim, Jinho; Yook, Soon-Hyung; Kim, Yup

2016-08-01

Spatial evolutionary games have mainly been studied on a single, isolated network. However, in real world systems, many interaction topologies are not isolated but many different types of networks are inter-connected to each other. In this study, we investigate the spatial evolutionary public goods game (SEPGG) on double-layered random networks (DRN). Based on the mean-field type arguments and numerical simulations, we find that SEPGG on DRN shows very rich interesting phenomena, especially, depending on the size of each layer, intra-connectivity, and inter-connected couplings, the network reciprocity of SEPGG on DRN can be drastically enhanced through the inter-connected coupling. Furthermore, SEPGG on DRN can provide a more general framework which includes the evolutionary dynamics on multiplex networks and inter-connected networks at the same time.

Reciprocity in spatial evolutionary public goods game on double-layered network

PubMed Central

Kim, Jinho; Yook, Soon-Hyung; Kim, Yup

2016-01-01

Spatial evolutionary games have mainly been studied on a single, isolated network. However, in real world systems, many interaction topologies are not isolated but many different types of networks are inter-connected to each other. In this study, we investigate the spatial evolutionary public goods game (SEPGG) on double-layered random networks (DRN). Based on the mean-field type arguments and numerical simulations, we find that SEPGG on DRN shows very rich interesting phenomena, especially, depending on the size of each layer, intra-connectivity, and inter-connected couplings, the network reciprocity of SEPGG on DRN can be drastically enhanced through the inter-connected coupling. Furthermore, SEPGG on DRN can provide a more general framework which includes the evolutionary dynamics on multiplex networks and inter-connected networks at the same time. PMID:27503801

Sequential interactions-in which one player plays first and another responds-promote cooperation in evolutionary-dynamical simulations of single-shot Prisoner's Dilemma and Snowdrift games.

PubMed

Laird, Robert A

2018-09-07

Cooperation is a central topic in evolutionary biology because (a) it is difficult to reconcile why individuals would act in a way that benefits others if such action is costly to themselves, and (b) it underpins many of the 'major transitions of evolution', making it essential for explaining the origins of successively higher levels of biological organization. Within evolutionary game theory, the Prisoner's Dilemma and Snowdrift games are the main theoretical constructs used to study the evolution of cooperation in dyadic interactions. In single-shot versions of these games, wherein individuals play each other only once, players typically act simultaneously rather than sequentially. Allowing one player to respond to the actions of its co-player-in the absence of any possibility of the responder being rewarded for cooperation or punished for defection, as in simultaneous or sequential iterated games-may seem to invite more incentive for exploitation and retaliation in single-shot games, compared to when interactions occur simultaneously, thereby reducing the likelihood that cooperative strategies can thrive. To the contrary, I use lattice-based, evolutionary-dynamical simulation models of single-shot games to demonstrate that under many conditions, sequential interactions have the potential to enhance unilaterally or mutually cooperative outcomes and increase the average payoff of populations, relative to simultaneous interactions-benefits that are especially prevalent in a spatially explicit context. This surprising result is attributable to the presence of conditional strategies that emerge in sequential games that can't occur in the corresponding simultaneous versions. Copyright © 2018 Elsevier Ltd. All rights reserved.

Games of life and death: antibiotic resistance and production through the lens of evolutionary game theory.

PubMed

Conlin, Peter L; Chandler, Josephine R; Kerr, Benjamin

2014-10-01

In this review, we demonstrate how game theory can be a useful first step in modeling and understanding interactions among bacteria that produce and resist antibiotics. We introduce the basic features of evolutionary game theory and explore model microbial systems that correspond to some classical games. Each game discussed defines a different category of social interaction with different resulting population dynamics (exclusion, coexistence, bistability, cycling). We then explore how the framework can be extended to incorporate some of the complexity of natural microbial communities. Overall, the game theoretical perspective helps to guide our expectations about the evolution of some forms of antibiotic resistance and production because it makes clear the precise nature of social interaction in this context. Copyright © 2014 Elsevier Ltd. All rights reserved.

Evolutionary dynamics and the phase structure of the minority game

NASA Astrophysics Data System (ADS)

Yuan, Baosheng; Chen, Kan

2004-06-01

We show that a simple evolutionary scheme, when applied to the minority game (MG), changes the phase structure of the game. In this scheme each agent evolves individually whenever his wealth reaches the specified bankruptcy level, in contrast to the evolutionary schemes used in the previous works. We show that evolution greatly suppresses herding behavior, and it leads to better overall performance of the agents. Similar to the standard nonevolutionary MG, the dependence of the standard deviation σ on the number of agents N and the memory length m can be characterized by a universal curve. We suggest a crowd-anticrowd theory for understanding the effect of evolution in the MG.

What Information Theory Says about Bounded Rational Best Response

NASA Technical Reports Server (NTRS)

Wolpert, David H.

2005-01-01

Probability Collectives (PC) provides the information-theoretic extension of conventional full-rationality game theory to bounded rational games. Here an explicit solution to the equations giving the bounded rationality equilibrium of a game is presented. Then PC is used to investigate games in which the players use bounded rational best-response strategies. Next it is shown that in the continuum-time limit, bounded rational best response games result in a variant of the replicator dynamics of evolutionary game theory. It is then shown that for team (shared-payoff) games, this variant of replicator dynamics is identical to Newton-Raphson iterative optimization of the shared utility function.

The evolutionary language game: an orthogonal approach.

PubMed

Lenaerts, Tom; Jansen, Bart; Tuyls, Karl; De Vylder, Bart

2005-08-21

Evolutionary game dynamics have been proposed as a mathematical framework for the cultural evolution of language and more specifically the evolution of vocabulary. This article discusses a model that is mutually exclusive in its underlying principals with some previously suggested models. The model describes how individuals in a population culturally acquire a vocabulary by actively participating in the acquisition process instead of passively observing and communicate through peer-to-peer interactions instead of vertical parent-offspring relations. Concretely, a notion of social/cultural learning called the naming game is first abstracted using learning theory. This abstraction defines the required cultural transmission mechanism for an evolutionary process. Second, the derived transmission system is expressed in terms of the well-known selection-mutation model defined in the context of evolutionary dynamics. In this way, the analogy between social learning and evolution at the level of meaning-word associations is made explicit. Although only horizontal and oblique transmission structures will be considered, extensions to vertical structures over different genetic generations can easily be incorporated. We provide a number of simplified experiments to clarify our reasoning.

Adaptive Topographies and Equilibrium Selection in an Evolutionary Game

PubMed Central

Osinga, Hinke M.; Marshall, James A. R.

2015-01-01

It has long been known in the field of population genetics that adaptive topographies, in which population equilibria maximise mean population fitness for a trait regardless of its genetic bases, do not exist. Whether one chooses to model selection acting on a single locus or multiple loci does matter. In evolutionary game theory, analysis of a simple and general game involving distinct roles for the two players has shown that whether strategies are modelled using a single ‘locus’ or one ‘locus’ for each role, the stable population equilibria are unchanged and correspond to the fitness-maximising evolutionary stable strategies of the game. This is curious given the aforementioned population genetical results on the importance of the genetic bases of traits. Here we present a dynamical systems analysis of the game with roles detailing how, while the stable equilibria in this game are unchanged by the number of ‘loci’ modelled, equilibrium selection may differ under the two modelling approaches. PMID:25706762

Dynamic fractals in spatial evolutionary games

NASA Astrophysics Data System (ADS)

Kolotev, Sergei; Malyutin, Aleksandr; Burovski, Evgeni; Krashakov, Sergei; Shchur, Lev

2018-06-01

We investigate critical properties of a spatial evolutionary game based on the Prisoner's Dilemma. Simulations demonstrate a jump in the component densities accompanied by drastic changes in average sizes of the component clusters. We argue that the cluster boundary is a random fractal. Our simulations are consistent with the fractal dimension of the boundary being equal to 2, and the cluster boundaries are hence asymptotically space filling as the system size increases.

Stochastic evolutionary voluntary public goods game with punishment in a Quasi-birth-and-death process.

PubMed

Quan, Ji; Liu, Wei; Chu, Yuqing; Wang, Xianjia

2017-11-23

Traditional replication dynamic model and the corresponding concept of evolutionary stable strategy (ESS) only takes into account whether the system can return to the equilibrium after being subjected to a small disturbance. In the real world, due to continuous noise, the ESS of the system may not be stochastically stable. In this paper, a model of voluntary public goods game with punishment is studied in a stochastic situation. Unlike the existing model, we describe the evolutionary process of strategies in the population as a generalized quasi-birth-and-death process. And we investigate the stochastic stable equilibrium (SSE) instead. By numerical experiments, we get all possible SSEs of the system for any combination of parameters, and investigate the influence of parameters on the probabilities of the system to select different equilibriums. It is found that in the stochastic situation, the introduction of the punishment and non-participation strategies can change the evolutionary dynamics of the system and equilibrium of the game. There is a large range of parameters that the system selects the cooperative states as its SSE with a high probability. This result provides us an insight and control method for the evolution of cooperation in the public goods game in stochastic situations.

The σ law of evolutionary dynamics in community-structured population.

PubMed

Tang, Changbing; Li, Xiang; Cao, Lang; Zhan, Jingyuan

2012-08-07

Evolutionary game dynamics in finite populations provide a new framework to understand the selection of traits with frequency-dependent fitness. Recently, a simple but fundamental law of evolutionary dynamics, which we call σ law, describes how to determine the selection between two competing strategies: in most evolutionary processes with two strategies, A and B, strategy A is favored over B in weak selection if and only if σR+S>T+σP. This relationship holds for a wide variety of structured populations with mutation rate and weak selection under certain assumptions. In this paper, we propose a model of games based on a community-structured population and revisit this law under the Moran process. By calculating the average payoffs of A and B individuals with the method of effective sojourn time, we find that σ features not only the structured population characteristics, but also the reaction rate between individuals. That is to say, an interaction between two individuals are not uniform, and we can take σ as a reaction rate between any two individuals with the same strategy. We verify this viewpoint by the modified replicator equation with non-uniform interaction rates in a simplified version of the prisoner's dilemma game (PDG). Copyright © 2012 Elsevier Ltd. All rights reserved.

Evolutionary potential games on lattices

NASA Astrophysics Data System (ADS)

Szabó, György; Borsos, István

2016-04-01

Game theory provides a general mathematical background to study the effect of pair interactions and evolutionary rules on the macroscopic behavior of multi-player games where players with a finite number of strategies may represent a wide scale of biological objects, human individuals, or even their associations. In these systems the interactions are characterized by matrices that can be decomposed into elementary matrices (games) and classified into four types. The concept of decomposition helps the identification of potential games and also the evaluation of the potential that plays a crucial role in the determination of the preferred Nash equilibrium, and defines the Boltzmann distribution towards which these systems evolve for suitable types of dynamical rules. This survey draws parallel between the potential games and the kinetic Ising type models which are investigated for a wide scale of connectivity structures. We discuss briefly the applicability of the tools and concepts of statistical physics and thermodynamics. Additionally the general features of ordering phenomena, phase transitions and slow relaxations are outlined and applied to evolutionary games. The discussion extends to games with three or more strategies. Finally we discuss what happens when the system is weakly driven out of the "equilibrium state" by adding non-potential components representing games of cyclic dominance.

Modeling Misbehavior in Cooperative Diversity: A Dynamic Game Approach

NASA Astrophysics Data System (ADS)

Dehnie, Sintayehu; Memon, Nasir

2009-12-01

Cooperative diversity protocols are designed with the assumption that terminals always help each other in a socially efficient manner. This assumption may not be valid in commercial wireless networks where terminals may misbehave for selfish or malicious intentions. The presence of misbehaving terminals creates a social-dilemma where terminals exhibit uncertainty about the cooperative behavior of other terminals in the network. Cooperation in social-dilemma is characterized by a suboptimal Nash equilibrium where wireless terminals opt out of cooperation. Hence, without establishing a mechanism to detect and mitigate effects of misbehavior, it is difficult to maintain a socially optimal cooperation. In this paper, we first examine effects of misbehavior assuming static game model and show that cooperation under existing cooperative protocols is characterized by a noncooperative Nash equilibrium. Using evolutionary game dynamics we show that a small number of mutants can successfully invade a population of cooperators, which indicates that misbehavior is an evolutionary stable strategy (ESS). Our main goal is to design a mechanism that would enable wireless terminals to select reliable partners in the presence of uncertainty. To this end, we formulate cooperative diversity as a dynamic game with incomplete information. We show that the proposed dynamic game formulation satisfied the conditions for the existence of perfect Bayesian equilibrium.

Integrating Evolutionary Game Theory into Mechanistic Genotype-Phenotype Mapping.

PubMed

Zhu, Xuli; Jiang, Libo; Ye, Meixia; Sun, Lidan; Gragnoli, Claudia; Wu, Rongling

2016-05-01

Natural selection has shaped the evolution of organisms toward optimizing their structural and functional design. However, how this universal principle can enhance genotype-phenotype mapping of quantitative traits has remained unexplored. Here we show that the integration of this principle and functional mapping through evolutionary game theory gains new insight into the genetic architecture of complex traits. By viewing phenotype formation as an evolutionary system, we formulate mathematical equations to model the ecological mechanisms that drive the interaction and coordination of its constituent components toward population dynamics and stability. Functional mapping provides a procedure for estimating the genetic parameters that specify the dynamic relationship of competition and cooperation and predicting how genes mediate the evolution of this relationship during trait formation. Copyright © 2016 Elsevier Ltd. All rights reserved.

Stochastic Evolution Dynamic of the Rock-Scissors-Paper Game Based on a Quasi Birth and Death Process

NASA Astrophysics Data System (ADS)

Yu, Qian; Fang, Debin; Zhang, Xiaoling; Jin, Chen; Ren, Qiyu

2016-06-01

Stochasticity plays an important role in the evolutionary dynamic of cyclic dominance within a finite population. To investigate the stochastic evolution process of the behaviour of bounded rational individuals, we model the Rock-Scissors-Paper (RSP) game as a finite, state dependent Quasi Birth and Death (QBD) process. We assume that bounded rational players can adjust their strategies by imitating the successful strategy according to the payoffs of the last round of the game, and then analyse the limiting distribution of the QBD process for the game stochastic evolutionary dynamic. The numerical experiments results are exhibited as pseudo colour ternary heat maps. Comparisons of these diagrams shows that the convergence property of long run equilibrium of the RSP game in populations depends on population size and the parameter of the payoff matrix and noise factor. The long run equilibrium is asymptotically stable, neutrally stable and unstable respectively according to the normalised parameters in the payoff matrix. Moreover, the results show that the distribution probability becomes more concentrated with a larger population size. This indicates that increasing the population size also increases the convergence speed of the stochastic evolution process while simultaneously reducing the influence of the noise factor.

Stochastic Evolution Dynamic of the Rock-Scissors-Paper Game Based on a Quasi Birth and Death Process.

PubMed

Yu, Qian; Fang, Debin; Zhang, Xiaoling; Jin, Chen; Ren, Qiyu

2016-06-27

Stochasticity plays an important role in the evolutionary dynamic of cyclic dominance within a finite population. To investigate the stochastic evolution process of the behaviour of bounded rational individuals, we model the Rock-Scissors-Paper (RSP) game as a finite, state dependent Quasi Birth and Death (QBD) process. We assume that bounded rational players can adjust their strategies by imitating the successful strategy according to the payoffs of the last round of the game, and then analyse the limiting distribution of the QBD process for the game stochastic evolutionary dynamic. The numerical experiments results are exhibited as pseudo colour ternary heat maps. Comparisons of these diagrams shows that the convergence property of long run equilibrium of the RSP game in populations depends on population size and the parameter of the payoff matrix and noise factor. The long run equilibrium is asymptotically stable, neutrally stable and unstable respectively according to the normalised parameters in the payoff matrix. Moreover, the results show that the distribution probability becomes more concentrated with a larger population size. This indicates that increasing the population size also increases the convergence speed of the stochastic evolution process while simultaneously reducing the influence of the noise factor.

A dynamic parking charge optimal control model under perspective of commuters' evolutionary game behavior

NASA Astrophysics Data System (ADS)

Lin, XuXun; Yuan, PengCheng

2018-01-01

In this research we consider commuters' dynamic learning effect by modeling the trip mode choice behavior from a new perspective of dynamic evolutionary game theory. We explore the behavior pattern of different types of commuters and study the evolution path and equilibrium properties under different traffic conditions. We further establish a dynamic parking charge optimal control (referred to as DPCOC) model to alter commuters' trip mode choice while minimizing the total social cost. Numerical tests show. (1) Under fixed parking fee policy, the evolutionary results are completely decided by the travel time and the only method for public transit induction is to increase the parking charge price. (2) Compared with fixed parking fee policy, DPCOC policy proposed in this research has several advantages. Firstly, it can effectively turn the evolutionary path and evolutionary stable strategy to a better situation while minimizing the total social cost. Secondly, it can reduce the sensitivity of trip mode choice behavior to traffic congestion and improve the ability to resist interferences and emergencies. Thirdly, it is able to control the private car proportion to a stable state and make the trip behavior more predictable for the transportation management department. The research results can provide theoretical basis and decision-making references for commuters' mode choice prediction, dynamic setting of urban parking charge prices and public transit induction.

Weight of fitness deviation governs strict physical chaos in replicator dynamics.

PubMed

Pandit, Varun; Mukhopadhyay, Archan; Chakraborty, Sagar

2018-03-01

Replicator equation-a paradigm equation in evolutionary game dynamics-mathematizes the frequency dependent selection of competing strategies vying to enhance their fitness (quantified by the average payoffs) with respect to the average fitnesses of the evolving population under consideration. In this paper, we deal with two discrete versions of the replicator equation employed to study evolution in a population where any two players' interaction is modelled by a two-strategy symmetric normal-form game. There are twelve distinct classes of such games, each typified by a particular ordinal relationship among the elements of the corresponding payoff matrix. Here, we find the sufficient conditions for the existence of asymptotic solutions of the replicator equations such that the solutions-fixed points, periodic orbits, and chaotic trajectories-are all strictly physical, meaning that the frequency of any strategy lies inside the closed interval zero to one at all times. Thus, we elaborate on which of the twelve types of games are capable of showing meaningful physical solutions and for which of the two types of replicator equation. Subsequently, we introduce the concept of the weight of fitness deviation that is the scaling factor in a positive affine transformation connecting two payoff matrices such that the corresponding one-shot games have exactly same Nash equilibria and evolutionary stable states. The weight also quantifies how much the excess of fitness of a strategy over the average fitness of the population affects the per capita change in the frequency of the strategy. Intriguingly, the weight's variation is capable of making the Nash equilibria and the evolutionary stable states, useless by introducing strict physical chaos in the replicator dynamics based on the normal-form game.

Some dynamics of signaling games.

PubMed

Huttegger, Simon; Skyrms, Brian; Tarrès, Pierre; Wagner, Elliott

2014-07-22

Information transfer is a basic feature of life that includes signaling within and between organisms. Owing to its interactive nature, signaling can be investigated by using game theory. Game theoretic models of signaling have a long tradition in biology, economics, and philosophy. For a long time the analyses of these games has mostly relied on using static equilibrium concepts such as Pareto optimal Nash equilibria or evolutionarily stable strategies. More recently signaling games of various types have been investigated with the help of game dynamics, which includes dynamical models of evolution and individual learning. A dynamical analysis leads to more nuanced conclusions as to the outcomes of signaling interactions. Here we explore different kinds of signaling games that range from interactions without conflicts of interest between the players to interactions where their interests are seriously misaligned. We consider these games within the context of evolutionary dynamics (both infinite and finite population models) and learning dynamics (reinforcement learning). Some results are specific features of a particular dynamical model, whereas others turn out to be quite robust across different models. This suggests that there are certain qualitative aspects that are common to many real-world signaling interactions.

Some dynamics of signaling games

PubMed Central

Huttegger, Simon; Skyrms, Brian; Tarrès, Pierre; Wagner, Elliott

2014-01-01

Information transfer is a basic feature of life that includes signaling within and between organisms. Owing to its interactive nature, signaling can be investigated by using game theory. Game theoretic models of signaling have a long tradition in biology, economics, and philosophy. For a long time the analyses of these games has mostly relied on using static equilibrium concepts such as Pareto optimal Nash equilibria or evolutionarily stable strategies. More recently signaling games of various types have been investigated with the help of game dynamics, which includes dynamical models of evolution and individual learning. A dynamical analysis leads to more nuanced conclusions as to the outcomes of signaling interactions. Here we explore different kinds of signaling games that range from interactions without conflicts of interest between the players to interactions where their interests are seriously misaligned. We consider these games within the context of evolutionary dynamics (both infinite and finite population models) and learning dynamics (reinforcement learning). Some results are specific features of a particular dynamical model, whereas others turn out to be quite robust across different models. This suggests that there are certain qualitative aspects that are common to many real-world signaling interactions. PMID:25024209

Applying evolutionary psychology to a serious game about children's interpersonal conflict.

PubMed

Ingram, Gordon P D; Campos, Joana; Hondrou, Charline; Vasalou, Asimina; Martinho, Carlos; Joinson, Adam

2012-12-20

This article describes the use of evolutionary psychology to inform the design of a serious computer game aimed at improving 9-12-year-old children's conflict resolution skills. The design of the game will include dynamic narrative generation and emotional tagging, and there is a strong evolutionary rationale for the effect of both of these on conflict resolution. Gender differences will also be taken into consideration in designing the game. In interview research in schools in three countries (Greece, Portugal, and the UK) aimed at formalizing the game requirements, we found that gender differences varied in the extent to which they applied cross-culturally. Across the three countries, girls were less likely to talk about responding to conflict with physical aggression, talked more about feeling sad about conflict and about conflicts over friendship alliances, and talked less about conflicts in the context of sports or games. Predicted gender differences in anger and reconciliation were not found. Results are interpreted in terms of differing underlying models of friendship that are motivated by parental investment theory. This research will inform the design of the themes that we use in game scenarios for both girls and boys.

Why Darwin would have loved evolutionary game theory

PubMed Central

2016-01-01

Humans have marvelled at the fit of form and function, the way organisms' traits seem remarkably suited to their lifestyles and ecologies. While natural selection provides the scientific basis for the fit of form and function, Darwin found certain adaptations vexing or particularly intriguing: sex ratios, sexual selection and altruism. The logic behind these adaptations resides in frequency-dependent selection where the value of a given heritable phenotype (i.e. strategy) to an individual depends upon the strategies of others. Game theory is a branch of mathematics that is uniquely suited to solving such puzzles. While game theoretic thinking enters into Darwin's arguments and those of evolutionists through much of the twentieth century, the tools of evolutionary game theory were not available to Darwin or most evolutionists until the 1970s, and its full scope has only unfolded in the last three decades. As a consequence, game theory is applied and appreciated rather spottily. Game theory not only applies to matrix games and social games, it also applies to speciation, macroevolution and perhaps even to cancer. I assert that life and natural selection are a game, and that game theory is the appropriate logic for framing and understanding adaptations. Its scope can include behaviours within species, state-dependent strategies (such as male, female and so much more), speciation and coevolution, and expands beyond microevolution to macroevolution. Game theory clarifies aspects of ecological and evolutionary stability in ways useful to understanding eco-evolutionary dynamics, niche construction and ecosystem engineering. In short, I would like to think that Darwin would have found game theory uniquely useful for his theory of natural selection. Let us see why this is so. PMID:27605503

Why Darwin would have loved evolutionary game theory.

PubMed

Brown, Joel S

2016-09-14

Humans have marvelled at the fit of form and function, the way organisms' traits seem remarkably suited to their lifestyles and ecologies. While natural selection provides the scientific basis for the fit of form and function, Darwin found certain adaptations vexing or particularly intriguing: sex ratios, sexual selection and altruism. The logic behind these adaptations resides in frequency-dependent selection where the value of a given heritable phenotype (i.e. strategy) to an individual depends upon the strategies of others. Game theory is a branch of mathematics that is uniquely suited to solving such puzzles. While game theoretic thinking enters into Darwin's arguments and those of evolutionists through much of the twentieth century, the tools of evolutionary game theory were not available to Darwin or most evolutionists until the 1970s, and its full scope has only unfolded in the last three decades. As a consequence, game theory is applied and appreciated rather spottily. Game theory not only applies to matrix games and social games, it also applies to speciation, macroevolution and perhaps even to cancer. I assert that life and natural selection are a game, and that game theory is the appropriate logic for framing and understanding adaptations. Its scope can include behaviours within species, state-dependent strategies (such as male, female and so much more), speciation and coevolution, and expands beyond microevolution to macroevolution. Game theory clarifies aspects of ecological and evolutionary stability in ways useful to understanding eco-evolutionary dynamics, niche construction and ecosystem engineering. In short, I would like to think that Darwin would have found game theory uniquely useful for his theory of natural selection. Let us see why this is so. © 2016 The Author(s).

A piecewise smooth model of evolutionary game for residential mobility and segregation

NASA Astrophysics Data System (ADS)

Radi, D.; Gardini, L.

2018-05-01

The paper proposes an evolutionary version of a Schelling-type dynamic system to model the patterns of residential segregation when two groups of people are involved. The payoff functions of agents are the individual preferences for integration which are empirically grounded. Differently from Schelling's model, where the limited levels of tolerance are the driving force of segregation, in the current setup agents benefit from integration. Despite the differences, the evolutionary model shows a dynamics of segregation that is qualitatively similar to the one of the classical Schelling's model: segregation is always a stable equilibrium, while equilibria of integration exist only for peculiar configurations of the payoff functions and their asymptotic stability is highly sensitive to parameter variations. Moreover, a rich variety of integrated dynamic behaviors can be observed. In particular, the dynamics of the evolutionary game is regulated by a one-dimensional piecewise smooth map with two kink points that is rigorously analyzed using techniques recently developed for piecewise smooth dynamical systems. The investigation reveals that when a stable internal equilibrium exists, the bimodal shape of the map leads to several different kinds of bifurcations, smooth, and border collision, in a complicated interplay. Our global analysis can give intuitions to be used by a social planner to maximize integration through social policies that manipulate people's preferences for integration.

Evolutionary game based control for biological systems with applications in drug delivery.

PubMed

Li, Xiaobo; Lenaghan, Scott C; Zhang, Mingjun

2013-06-07

Control engineering and analysis of biological systems have become increasingly important for systems and synthetic biology. Unfortunately, no widely accepted control framework is currently available for these systems, especially at the cell and molecular levels. This is partially due to the lack of appropriate mathematical models to describe the unique dynamics of biological systems, and the lack of implementation techniques, such as ultra-fast and ultra-small devices and corresponding control algorithms. This paper proposes a control framework for biological systems subject to dynamics that exhibit adaptive behavior under evolutionary pressures. The control framework was formulated based on evolutionary game based modeling, which integrates both the internal dynamics and the population dynamics. In the proposed control framework, the adaptive behavior was characterized as an internal dynamic, and the external environment was regarded as an external control input. The proposed open-interface control framework can be integrated with additional control algorithms for control of biological systems. To demonstrate the effectiveness of the proposed framework, an optimal control strategy was developed and validated for drug delivery using the pathogen Giardia lamblia as a test case. In principle, the proposed control framework can be applied to any biological system exhibiting adaptive behavior under evolutionary pressures. Copyright © 2013 Elsevier Ltd. All rights reserved.

Topological chaos of the spatial prisoner's dilemma game on regular networks.

PubMed

Jin, Weifeng; Chen, Fangyue

2016-02-21

The spatial version of evolutionary prisoner's dilemma on infinitely large regular lattice with purely deterministic strategies and no memories among players is investigated in this paper. Based on the statistical inferences, it is pertinent to confirm that the frequency of cooperation for characterizing its macroscopic behaviors is very sensitive to the initial conditions, which is the most practically significant property of chaos. Its intrinsic complexity is then justified on firm ground from the theory of symbolic dynamics; that is, this game is topologically mixing and possesses positive topological entropy on its subsystems. It is demonstrated therefore that its frequency of cooperation could not be adopted by simply averaging over several steps after the game reaches the equilibrium state. Furthermore, the chaotically changing spatial patterns via empirical observations can be defined and justified in view of symbolic dynamics. It is worth mentioning that the procedure proposed in this work is also applicable to other deterministic spatial evolutionary games therein. Copyright © 2015 Elsevier Ltd. All rights reserved.

An Evolutionary Game Theory Model of Spontaneous Brain Functioning.

PubMed

Madeo, Dario; Talarico, Agostino; Pascual-Leone, Alvaro; Mocenni, Chiara; Santarnecchi, Emiliano

2017-11-22

Our brain is a complex system of interconnected regions spontaneously organized into distinct networks. The integration of information between and within these networks is a continuous process that can be observed even when the brain is at rest, i.e. not engaged in any particular task. Moreover, such spontaneous dynamics show predictive value over individual cognitive profile and constitute a potential marker in neurological and psychiatric conditions, making its understanding of fundamental importance in modern neuroscience. Here we present a theoretical and mathematical model based on an extension of evolutionary game theory on networks (EGN), able to capture brain's interregional dynamics by balancing emulative and non-emulative attitudes among brain regions. This results in the net behavior of nodes composing resting-state networks identified using functional magnetic resonance imaging (fMRI), determining their moment-to-moment level of activation and inhibition as expressed by positive and negative shifts in BOLD fMRI signal. By spontaneously generating low-frequency oscillatory behaviors, the EGN model is able to mimic functional connectivity dynamics, approximate fMRI time series on the basis of initial subset of available data, as well as simulate the impact of network lesions and provide evidence of compensation mechanisms across networks. Results suggest evolutionary game theory on networks as a new potential framework for the understanding of human brain network dynamics.

Dilemma strength as a framework for advancing evolutionary game theory. Reply to comments on "Universal scaling for the dilemma strength in evolutionary games"

NASA Astrophysics Data System (ADS)

Wang, Zhen; Kokubo, Satoshi; Jusup, Marko; Tanimoto, Jun

2015-09-01

While comprehensive reviews of the literature, by gathering in one place most of the relevant information, undoubtedly steer the development of every scientific field, we found that the comments in response to a review article can be as informative as the review itself, if not more. Namely, reading through the comments on the ideas expressed in Ref. [1], we could identify a number of pressing problems for evolutionary game theory, indicating just how much space there still is for major advances and breakthroughs. In an attempt to bring a sense of order to a multitude of opinions, we roughly classified the comments into three categories, i.e. those concerned with: (i) the universality of scaling in heterogeneous topologies, including empirical dynamic networks [2-8], (ii) the universality of scaling for more general game setups, such as the inclusion of multiple strategies and external features [4,9-11], and (iii) experimental confirmations of the theoretical developments [2,12,13].

Evolutionary games of condensates in coupled birth–death processes

PubMed Central

Knebel, Johannes; Weber, Markus F.; Krüger, Torben; Frey, Erwin

2015-01-01

Condensation phenomena arise through a collective behaviour of particles. They are observed in both classical and quantum systems, ranging from the formation of traffic jams in mass transport models to the macroscopic occupation of the energetic ground state in ultra-cold bosonic gases (Bose–Einstein condensation). Recently, it has been shown that a driven and dissipative system of bosons may form multiple condensates. Which states become the condensates has, however, remained elusive thus far. The dynamics of this condensation are described by coupled birth–death processes, which also occur in evolutionary game theory. Here we apply concepts from evolutionary game theory to explain the formation of multiple condensates in such driven-dissipative bosonic systems. We show that the vanishing of relative entropy production determines their selection. The condensation proceeds exponentially fast, but the system never comes to rest. Instead, the occupation numbers of condensates may oscillate, as we demonstrate for a rock–paper–scissors game of condensates. PMID:25908384

A holistic image segmentation framework for cloud detection and extraction

NASA Astrophysics Data System (ADS)

Shen, Dan; Xu, Haotian; Blasch, Erik; Horvath, Gregory; Pham, Khanh; Zheng, Yufeng; Ling, Haibin; Chen, Genshe

2013-05-01

Atmospheric clouds are commonly encountered phenomena affecting visual tracking from air-borne or space-borne sensors. Generally clouds are difficult to detect and extract because they are complex in shape and interact with sunlight in a complex fashion. In this paper, we propose a clustering game theoretic image segmentation based approach to identify, extract, and patch clouds. In our framework, the first step is to decompose a given image containing clouds. The problem of image segmentation is considered as a "clustering game". Within this context, the notion of a cluster is equivalent to a classical equilibrium concept from game theory, as the game equilibrium reflects both the internal and external (e.g., two-player) cluster conditions. To obtain the evolutionary stable strategies, we explore three evolutionary dynamics: fictitious play, replicator dynamics, and infection and immunization dynamics (InImDyn). Secondly, we use the boundary and shape features to refine the cloud segments. This step can lower the false alarm rate. In the third step, we remove the detected clouds and patch the empty spots by performing background recovery. We demonstrate our cloud detection framework on a video clip provides supportive results.

Ecological theatre and the evolutionary game: how environmental and demographic factors determine payoffs in evolutionary games.

PubMed

Argasinski, K; Broom, M

2013-10-01

In the standard approach to evolutionary games and replicator dynamics, differences in fitness can be interpreted as an excess from the mean Malthusian growth rate in the population. In the underlying reasoning, related to an analysis of "costs" and "benefits", there is a silent assumption that fitness can be described in some type of units. However, in most cases these units of measure are not explicitly specified. Then the question arises: are these theories testable? How can we measure "benefit" or "cost"? A natural language, useful for describing and justifying comparisons of strategic "cost" versus "benefits", is the terminology of demography, because the basic events that shape the outcome of natural selection are births and deaths. In this paper, we present the consequences of an explicit analysis of births and deaths in an evolutionary game theoretic framework. We will investigate different types of mortality pressures, their combinations and the possibility of trade-offs between mortality and fertility. We will show that within this new approach it is possible to model how strictly ecological factors such as density dependence and additive background fitness, which seem neutral in classical theory, can affect the outcomes of the game. We consider the example of the Hawk-Dove game, and show that when reformulated in terms of our new approach new details and new biological predictions are produced.

Theoretical Approaches in Evolutionary Ecology: Environmental Feedback as a Unifying Perspective.

PubMed

Lion, Sébastien

2018-01-01

Evolutionary biology and ecology have a strong theoretical underpinning, and this has fostered a variety of modeling approaches. A major challenge of this theoretical work has been to unravel the tangled feedback loop between ecology and evolution. This has prompted the development of two main classes of models. While quantitative genetics models jointly consider the ecological and evolutionary dynamics of a focal population, a separation of timescales between ecology and evolution is assumed by evolutionary game theory, adaptive dynamics, and inclusive fitness theory. As a result, theoretical evolutionary ecology tends to be divided among different schools of thought, with different toolboxes and motivations. My aim in this synthesis is to highlight the connections between these different approaches and clarify the current state of theory in evolutionary ecology. Central to this approach is to make explicit the dependence on environmental dynamics of the population and evolutionary dynamics, thereby materializing the eco-evolutionary feedback loop. This perspective sheds light on the interplay between environmental feedback and the timescales of ecological and evolutionary processes. I conclude by discussing some potential extensions and challenges to our current theoretical understanding of eco-evolutionary dynamics.

The Dynamics of Information Transfer

ERIC Educational Resources Information Center

Wagner, Elliott

2012-01-01

Philosophers and scientists have long debated how communication can arise in circumstances in which it is not already present. This dissertation uses the techniques of evolutionary game theory to address this puzzle. Following David Lewis (1969), communication is envisioned as occurring between players in a game. One player, who has private…

The amazing evolutionary dynamics of non-linear optical systems with feedback

NASA Astrophysics Data System (ADS)

Yaroslavsky, Leonid

2013-09-01

Optical systems with feedback are, generally, non-linear dynamic systems. As such, they exhibit evolutionary behavior. In the paper we present results of experimental investigation of evolutionary dynamics of several models of such systems. The models are modifications of the famous mathematical "Game of Life". The modifications are two-fold: "Game of Life" rules are made stochastic and mutual influence of cells is made spatially non-uniform. A number of new phenomena in the evolutionary dynamics of the models are revealed: - "Ordering of chaos". Formation, from seed patterns, of stable maze-like patterns with chaotic "dislocations" that resemble natural patterns, such as skin patterns of some animals and fishes, see shell, fingerprints, magnetic domain patterns and alike, which one can frequently find in the nature. These patterns and their fragments exhibit a remarkable capability of unlimited growth. - "Self-controlled growth" of chaotic "live" formations into "communities" bounded, depending on the model, by a square, hexagon or octagon, until they reach a certain critical size, after which the growth stops. - "Eternal life in a bounded space" of "communities" after reaching a certain size and shape. - "Coherent shrinkage" of "mature", after reaching a certain size, "communities" into one of stable or oscillating patterns preserving in this process isomorphism of their bounding shapes until the very end.

Extinction rates in tumour public goods games.

PubMed

Gerlee, Philip; Altrock, Philipp M

2017-09-01

Cancer evolution and progression are shaped by cellular interactions and Darwinian selection. Evolutionary game theory incorporates both of these principles, and has been proposed as a framework to understand tumour cell population dynamics. A cornerstone of evolutionary dynamics is the replicator equation, which describes changes in the relative abundance of different cell types, and is able to predict evolutionary equilibria. Typically, the replicator equation focuses on differences in relative fitness. We here show that this framework might not be sufficient under all circumstances, as it neglects important aspects of population growth. Standard replicator dynamics might miss critical differences in the time it takes to reach an equilibrium, as this time also depends on cellular turnover in growing but bounded populations. As the system reaches a stable manifold, the time to reach equilibrium depends on cellular death and birth rates. These rates shape the time scales, in particular, in coevolutionary dynamics of growth factor producers and free-riders. Replicator dynamics might be an appropriate framework only when birth and death rates are of similar magnitude. Otherwise, population growth effects cannot be neglected when predicting the time to reach an equilibrium, and cell-type-specific rates have to be accounted for explicitly. © 2017 The Authors.

Evolution and social epidemiology.

PubMed

Nishi, Akihiro

2015-11-01

Evolutionary biology, which aims to explain the dynamic process of shaping the diversity of life, has not yet significantly affected thinking in social epidemiology. Current challenges in social epidemiology include understanding how social exposures can affect our biology, explaining the dynamics of society and health, and designing better interventions that are mindful of the impact of exposures during critical periods. I review how evolutionary concepts and tools, such as fitness gradient in cultural evolution, evolutionary game theory, and contemporary evolution in cancer, can provide helpful insights regarding social epidemiology. Copyright © 2015 Elsevier Ltd. All rights reserved.

Application of evolutionary games to modeling carcinogenesis.

PubMed

Swierniak, Andrzej; Krzeslak, Michal

2013-06-01

We review a quite large volume of literature concerning mathematical modelling of processes related to carcinogenesis and the growth of cancer cell populations based on the theory of evolutionary games. This review, although partly idiosyncratic, covers such major areas of cancer-related phenomena as production of cytotoxins, avoidance of apoptosis, production of growth factors, motility and invasion, and intra- and extracellular signaling. We discuss the results of other authors and append to them some additional results of our own simulations dealing with the possible dynamics and/or spatial distribution of the processes discussed.

Evolving learning rules and emergence of cooperation in spatial prisoner's dilemma.

PubMed

Moyano, Luis G; Sánchez, Angel

2009-07-07

In the evolutionary Prisoner's dilemma (PD) game, agents play with each other and update their strategies in every generation according to some microscopic dynamical rule. In its spatial version, agents do not play with every other but, instead, interact only with their neighbours, thus mimicking the existing of a social or contact network that defines who interacts with whom. In this work, we explore evolutionary, spatial PD systems consisting of two types of agents, each with a certain update (reproduction, learning) rule. We investigate two different scenarios: in the first case, update rules remain fixed for the entire evolution of the system; in the second case, agents update both strategy and update rule in every generation. We show that in a well-mixed population the evolutionary outcome is always full defection. We subsequently focus on two-strategy competition with nearest-neighbour interactions on the contact network and synchronised update of strategies. Our results show that, for an important range of the parameters of the game, the final state of the system is largely different from that arising from the usual setup of a single, fixed dynamical rule. Furthermore, the results are also very different if update rules are fixed or evolve with the strategies. In these respect, we have studied representative update rules, finding that some of them may become extinct while others prevail. We describe the new and rich variety of final outcomes that arise from this co-evolutionary dynamics. We include examples of other neighbourhoods and asynchronous updating that confirm the robustness of our conclusions. Our results pave the way to an evolutionary rationale for modelling social interactions through game theory with a preferred set of update rules.

Older partner selection promotes the prevalence of cooperation in evolutionary games.

PubMed

Yang, Guoli; Huang, Jincai; Zhang, Weiming

2014-10-21

Evolutionary games typically come with the interplays between evolution of individual strategy and adaptation to network structure. How these dynamics in the co-evolution promote (or obstruct) the cooperation is regarded as an important topic in social, economic, and biological fields. Combining spatial selection with partner choice, the focus of this paper is to identify which neighbour should be selected as a role to imitate during the process of co-evolution. Age, an internal attribute and kind of local piece of information regarding the survivability of the agent, is a significant consideration for the selection strategy. The analysis and simulations presented, demonstrate that older partner selection for strategy imitation could foster the evolution of cooperation. The younger partner selection, however, may decrease the level of cooperation. Our model highlights the importance of agent׳s age on the promotion of cooperation in evolutionary games, both efficiently and effectively. Copyright © 2014 Elsevier Ltd. All rights reserved.

Evolutionary game analysis and regulatory strategies for online group-buying based on system dynamics

NASA Astrophysics Data System (ADS)

Jiang, Zhong-Zhong; He, Na; Qin, Xuwei; Ip, W. H.; Wu, C. H.; Yung, K. L.

2018-07-01

The emergence of online group-buying provides a new consumption pattern for consumers in e-commerce era. However, many consumers realize that their own interests sometimes can't be guaranteed in the group-buying market due to the lack of being regulated. This paper aims to develop effective regulation strategies for online group-buying market. To the best of our knowledge, most existing studies assume that three parties in online group-buying market, i.e. the retailer, the group-buying platform and the consumer, are perfectly rational. To better understand the decision process, in this paper, we incorporate the concept of bounded rationality into consideration. Firstly, a three-parties evolutionary game model is established to study each player's game strategy based on bounded rationality. Secondly, the game model is simulated as a whole by adopting system dynamics to analyze its stability. Finally, theoretical analysis and extensive computational experiments are conducted to obtain the managerial insights and regulation strategies for online group-buying market. Our results clearly demonstrate that a suitable bonus-penalty measure can promote the healthy development of online group-buying market.

The Effects of Sacred Value Networks Within an Evolutionary, Adversarial Game

NASA Astrophysics Data System (ADS)

McCalla, Scott G.; Short, Martin B.; Brantingham, P. Jeffrey

2013-05-01

The effects of personal relationships and shared ideologies on levels of crime and the formation of criminal coalitions are studied within the context of an adversarial, evolutionary game first introduced in Short et al. (Phys. Rev. E 82:066114, 2010). Here, we interpret these relationships as connections on a graph of N players. These connections are then used in a variety of ways to define each player's "sacred value network"—groups of individuals that are subject to special consideration or treatment by that player. We explore the effects on the dynamics of the system that these networks introduce, through various forms of protection from both victimization and punishment. Under local protection, these networks introduce a new fixed point within the game dynamics, which we find through a continuum approximation of the discrete game. Under more complicated, extended protection, we numerically observe the emergence of criminal coalitions, or "gangs". We also find that a high-crime steady state is much more frequent in the context of extended protection networks, in both the case of Erdős-Rényi and small world random graphs.

Fostering cooperation of selfish agents through public goods in relation to the loners

NASA Astrophysics Data System (ADS)

Zhang, Jianlei; Chen, Zengqiang; Liu, Zhongxin

2016-03-01

Altruistic behaviors in multiplayer groups have obtained great attention in the context of the public goods game, which poses a riddle from the evolutionary viewpoint. Here we focus on a particular type of public goods game model in which the benefits of cooperation are either discounted or synergistically enhanced at the appearance of multiple cooperators in a group. Moreover, we focus on the three-strategies profile by adding the role of loners, besides the often-used cooperation and defection. Using the replicator dynamic equations, we investigate a range of dynamical portraits that characterizes the properties of the steady state. Analysis results indicate that loners and cooperators both have chances to be the stable equilibrium points in the presence of perturbations, while defectors fail to do so in this three-strategy competition. Moreover, the coexistence state, in which all three strategies exist in equilibrium, can be led by suitable parameters and stabilized for perturbations. These results elucidate the interplay between the characteristics of the public goods game and evolutionary dynamics in well-mixed systems.

Neighbourhood reaction in the evolution of cooperation.

PubMed

Yang, Guoli; Zhang, Weiming; Xiu, Baoxin

2015-05-07

Combining evolutionary games with adaptive networks, an entangled model between strategy evolution and structure adaptation is researched in this paper. We consider a large population of cooperators C and defectors D placed in the networks, playing the repeated prisoner׳s dilemma (PD) games. Because of the conflicts between social welfare and personal rationality, both strategy and structure are allowed to change. In this paper, the dynamics of strategy originates form the partner imitation based on social learning and the dynamics of structure is driven by the active linking and neighbourhood reaction. Notably, the neighbourhood reaction is investigated considering the changes of interfaces between cooperators and defectors, where some neighbours may get away from the interface once the focal agent changes to different strategy. A rich landscape is demonstrated by changing various embedding parameters, which sheds light upon that reacting promptly to the shifted neighbour will promote the prevalence of cooperation. Our model encapsulates the dynamics of strategy, reaction and structure into the evolutionary games, which manifests some intriguing principles in the competition between two groups in natural populations, artificial systems and even human societies. Copyright © 2015 Elsevier Ltd. All rights reserved.

Fixation of strategies with the Moran and Fermi processes in evolutionary games

NASA Astrophysics Data System (ADS)

Liu, Xuesong; He, Mingfeng; Kang, Yibin; Pan, Qiuhui

2017-10-01

A model of stochastic evolutionary game dynamics with finite population was built. It combines the standard Moran and Fermi rules with two strategies cooperation and defection. We obtain the expressions of fixation probabilities and fixation times. The one-third rule which has been found in the frequency dependent Moran process also holds for our model. We obtain the conditions of strategy being an evolutionarily stable strategy in our model, and then make a comparison with the standard Moran process. Besides, the analytical results show that compared with the standard Moran process, fixation occurs with higher probabilities under a prisoner's dilemma game and coordination game, but with lower probabilities under a coexistence game. The simulation result shows that the fixation time in our mixed process is lower than that in the standard Fermi process. In comparison with the standard Moran process, fixation always takes more time on average in spatial populations, regardless of the game. In addition, the fixation time decreases with the growth of the number of neighbors.

Learning and dynamics in social systems. Comment on "Collective learning modeling based on the kinetic theory of active particles" by D. Burini et al.

NASA Astrophysics Data System (ADS)

Dolfin, Marina

2016-03-01

The interesting novelty of the paper by Burini et al. [1] is that the authors present a survey and a new approach of collective learning based on suitable development of methods of the kinetic theory [2] and theoretical tools of evolutionary game theory [3]. Methods of statistical dynamics and kinetic theory lead naturally to stochastic and collective dynamics. Indeed, the authors propose the use of games where the state of the interacting entities is delivered by probability distributions.

Cyclic dominance in evolutionary games: a review

PubMed Central

Szolnoki, Attila; Mobilia, Mauro; Jiang, Luo-Luo; Szczesny, Bartosz; Rucklidge, Alastair M.; Perc, Matjaž

2014-01-01

Rock is wrapped by paper, paper is cut by scissors and scissors are crushed by rock. This simple game is popular among children and adults to decide on trivial disputes that have no obvious winner, but cyclic dominance is also at the heart of predator–prey interactions, the mating strategy of side-blotched lizards, the overgrowth of marine sessile organisms and competition in microbial populations. Cyclical interactions also emerge spontaneously in evolutionary games entailing volunteering, reward, punishment, and in fact are common when the competing strategies are three or more, regardless of the particularities of the game. Here, we review recent advances on the rock–paper–scissors (RPS) and related evolutionary games, focusing, in particular, on pattern formation, the impact of mobility and the spontaneous emergence of cyclic dominance. We also review mean-field and zero-dimensional RPS models and the application of the complex Ginzburg–Landau equation, and we highlight the importance and usefulness of statistical physics for the successful study of large-scale ecological systems. Directions for future research, related, for example, to dynamical effects of coevolutionary rules and invasion reversals owing to multi-point interactions, are also outlined. PMID:25232048

Cyclic dominance in evolutionary games: a review.

PubMed

Szolnoki, Attila; Mobilia, Mauro; Jiang, Luo-Luo; Szczesny, Bartosz; Rucklidge, Alastair M; Perc, Matjaž

2014-11-06

Rock is wrapped by paper, paper is cut by scissors and scissors are crushed by rock. This simple game is popular among children and adults to decide on trivial disputes that have no obvious winner, but cyclic dominance is also at the heart of predator-prey interactions, the mating strategy of side-blotched lizards, the overgrowth of marine sessile organisms and competition in microbial populations. Cyclical interactions also emerge spontaneously in evolutionary games entailing volunteering, reward, punishment, and in fact are common when the competing strategies are three or more, regardless of the particularities of the game. Here, we review recent advances on the rock-paper-scissors (RPS) and related evolutionary games, focusing, in particular, on pattern formation, the impact of mobility and the spontaneous emergence of cyclic dominance. We also review mean-field and zero-dimensional RPS models and the application of the complex Ginzburg-Landau equation, and we highlight the importance and usefulness of statistical physics for the successful study of large-scale ecological systems. Directions for future research, related, for example, to dynamical effects of coevolutionary rules and invasion reversals owing to multi-point interactions, are also outlined. © 2014 The Author(s) Published by the Royal Society. All rights reserved.

Weight of fitness deviation governs strict physical chaos in replicator dynamics

NASA Astrophysics Data System (ADS)

Pandit, Varun; Mukhopadhyay, Archan; Chakraborty, Sagar

2018-03-01

Replicator equation—a paradigm equation in evolutionary game dynamics—mathematizes the frequency dependent selection of competing strategies vying to enhance their fitness (quantified by the average payoffs) with respect to the average fitnesses of the evolving population under consideration. In this paper, we deal with two discrete versions of the replicator equation employed to study evolution in a population where any two players' interaction is modelled by a two-strategy symmetric normal-form game. There are twelve distinct classes of such games, each typified by a particular ordinal relationship among the elements of the corresponding payoff matrix. Here, we find the sufficient conditions for the existence of asymptotic solutions of the replicator equations such that the solutions—fixed points, periodic orbits, and chaotic trajectories—are all strictly physical, meaning that the frequency of any strategy lies inside the closed interval zero to one at all times. Thus, we elaborate on which of the twelve types of games are capable of showing meaningful physical solutions and for which of the two types of replicator equation. Subsequently, we introduce the concept of the weight of fitness deviation that is the scaling factor in a positive affine transformation connecting two payoff matrices such that the corresponding one-shot games have exactly same Nash equilibria and evolutionary stable states. The weight also quantifies how much the excess of fitness of a strategy over the average fitness of the population affects the per capita change in the frequency of the strategy. Intriguingly, the weight's variation is capable of making the Nash equilibria and the evolutionary stable states, useless by introducing strict physical chaos in the replicator dynamics based on the normal-form game.

Evidence Combination From an Evolutionary Game Theory Perspective.

PubMed

Deng, Xinyang; Han, Deqiang; Dezert, Jean; Deng, Yong; Shyr, Yu

2016-09-01

Dempster-Shafer evidence theory is a primary methodology for multisource information fusion because it is good at dealing with uncertain information. This theory provides a Dempster's rule of combination to synthesize multiple evidences from various information sources. However, in some cases, counter-intuitive results may be obtained based on that combination rule. Numerous new or improved methods have been proposed to suppress these counter-intuitive results based on perspectives, such as minimizing the information loss or deviation. Inspired by evolutionary game theory, this paper considers a biological and evolutionary perspective to study the combination of evidences. An evolutionary combination rule (ECR) is proposed to help find the most biologically supported proposition in a multievidence system. Within the proposed ECR, we develop a Jaccard matrix game to formalize the interaction between propositions in evidences, and utilize the replicator dynamics to mimick the evolution of propositions. Experimental results show that the proposed ECR can effectively suppress the counter-intuitive behaviors appeared in typical paradoxes of evidence theory, compared with many existing methods. Properties of the ECR, such as solution's stability and convergence, have been mathematically proved as well.

Analysis of Managing Safety in Small Enterprises: Dual-Effects of Employee Prosocial Safety Behavior and Government Inspection

PubMed Central

2018-01-01

This paper aims to promote a national and international occupational health and safety (OHS) intervention for small and medium enterprises (SMEs) within internal and external resources. Based on the characteristics of small SME management, the work environment and occupational health may be positively affected by the dual-effects of employees and government. Evolutionary game theory is utilized to identify relevant interactions among the government, small enterprises, and employees. Furthermore, dynamic simulations of the evolutionary game model are used to explore stability strategies and to identify modes of equilibrium. PMID:29707574

The role of noise in the spatial public goods game

NASA Astrophysics Data System (ADS)

Javarone, Marco Alberto; Battiston, Federico

2016-07-01

In this work we aim to analyze the role of noise in the spatial public goods game, one of the most famous games in evolutionary game theory. The dynamics of this game is affected by a number of parameters and processes, namely the topology of interactions among the agents, the synergy factor, and the strategy revision phase. The latter is a process that allows agents to change their strategy. Notably, rational agents tend to imitate richer neighbors, in order to increase the probability to maximize their payoff. By implementing a stochastic revision process, it is possible to control the level of noise in the system, so that even irrational updates may occur. In particular, in this work we study the effect of noise on the macroscopic behavior of a finite structured population playing the public goods game. We consider both the case of a homogeneous population, where the noise in the system is controlled by tuning a parameter representing the level of stochasticity in the strategy revision phase, and a heterogeneous population composed of a variable proportion of rational and irrational agents. In both cases numerical investigations show that the public goods game has a very rich behavior which strongly depends on the amount of noise in the system and on the value of the synergy factor. To conclude, our study sheds a new light on the relations between the microscopic dynamics of the public goods game and its macroscopic behavior, strengthening the link between the field of evolutionary game theory and statistical physics.

Mutation-selection equilibrium in games with multiple strategies.

PubMed

Antal, Tibor; Traulsen, Arne; Ohtsuki, Hisashi; Tarnita, Corina E; Nowak, Martin A

2009-06-21

In evolutionary games the fitness of individuals is not constant but depends on the relative abundance of the various strategies in the population. Here we study general games among n strategies in populations of large but finite size. We explore stochastic evolutionary dynamics under weak selection, but for any mutation rate. We analyze the frequency dependent Moran process in well-mixed populations, but almost identical results are found for the Wright-Fisher and Pairwise Comparison processes. Surprisingly simple conditions specify whether a strategy is more abundant on average than 1/n, or than another strategy, in the mutation-selection equilibrium. We find one condition that holds for low mutation rate and another condition that holds for high mutation rate. A linear combination of these two conditions holds for any mutation rate. Our results allow a complete characterization of nxn games in the limit of weak selection.

Mutation-selection equilibrium in games with mixed strategies.

PubMed

Tarnita, Corina E; Antal, Tibor; Nowak, Martin A

2009-11-07

We develop a new method for studying stochastic evolutionary game dynamics of mixed strategies. We consider the general situation: there are n pure strategies whose interactions are described by an nxn payoff matrix. Players can use mixed strategies, which are given by the vector (p(1),...,p(n)). Each entry specifies the probability to use the corresponding pure strategy. The sum over all entries is one. Therefore, a mixed strategy is a point in the simplex S(n). We study evolutionary dynamics in a well-mixed population of finite size. Individuals reproduce proportional to payoff. We consider the case of weak selection, which means the payoff from the game is only a small contribution to overall fitness. Reproduction can be subject to mutation; a mutant adopts a randomly chosen mixed strategy. We calculate the average abundance of every mixed strategy in the stationary distribution of the mutation-selection process. We find the crucial conditions that specify if a strategy is favored or opposed by selection. One condition holds for low mutation rate, another for high mutation rate. The result for any mutation rate is a linear combination of those two. As a specific example we study the Hawk-Dove game. We prove general statements about the relationship between games with pure and with mixed strategies.

Testability of evolutionary game dynamics based on experimental economics data

NASA Astrophysics Data System (ADS)

Wang, Yijia; Chen, Xiaojie; Wang, Zhijian

In order to better understand the dynamic processes of a real game system, we need an appropriate dynamics model, so to evaluate the validity of a model is not a trivial task. Here, we demonstrate an approach, considering the dynamical macroscope patterns of angular momentum and speed as the measurement variables, to evaluate the validity of various dynamics models. Using the data in real time Rock-Paper-Scissors (RPS) games experiments, we obtain the experimental dynamic patterns, and then derive the related theoretical dynamic patterns from a series of typical dynamics models respectively. By testing the goodness-of-fit between the experimental and theoretical patterns, the validity of the models can be evaluated. One of the results in our study case is that, among all the nonparametric models tested, the best-known Replicator dynamics model performs almost worst, while the Projection dynamics model performs best. Besides providing new empirical macroscope patterns of social dynamics, we demonstrate that the approach can be an effective and rigorous tool to test game dynamics models. Fundamental Research Funds for the Central Universities (SSEYI2014Z) and the National Natural Science Foundation of China (Grants No. 61503062).

Polymorphic Evolutionary Games.

PubMed

Fishman, Michael A

2016-06-07

In this paper, I present an analytical framework for polymorphic evolutionary games suitable for explicitly modeling evolutionary processes in diploid populations with sexual reproduction. The principal aspect of the proposed approach is adding diploid genetics cum sexual recombination to a traditional evolutionary game, and switching from phenotypes to haplotypes as the new game׳s pure strategies. Here, the relevant pure strategy׳s payoffs derived by summing the payoffs of all the phenotypes capable of producing gametes containing that particular haplotype weighted by the pertinent probabilities. The resulting game is structurally identical to the familiar Evolutionary Games with non-linear pure strategy payoffs (Hofbauer and Sigmund, 1998. Cambridge University Press), and can be analyzed in terms of an established analytical framework for such games. And these results can be translated into the terms of genotypic, and whence, phenotypic evolutionary stability pertinent to the original game. Copyright © 2016 Elsevier Ltd. All rights reserved.

Randomness and arbitrary coordination in the reactive ultimatum game

NASA Astrophysics Data System (ADS)

da Silva, Roberto; Valverde, Pablo; Lamb, Luis C.

2016-07-01

Darwin's theory of evolution - as introduced in game theory by Maynard Smith - is not the only important evolutionary aspect in an evolutionary dynamics, since complex interdependencies, competition, and growth should be modeled by, for example, reactive aspects. In the ultimatum game, the reciprocity and the fifty-fifty partition seems to be a deviation from rational behavior of the players under the light of Nash equilibrium. Such equilibrium emerges, for example, from the punishment of the responder who generally tends to refuse unfair proposals. In the iterated version of the game, the proposers are able to improve their proposals by adding a value thus making fairer proposals. Such evolutionary aspects are not properly Darwinian-motivated, but they are endowed with a fundamental aspect: they reflect their actions according to value of the offers. Recently, a reactive version of the ultimatum game where acceptance occurs with fixed probability was proposed. In this paper, we aim at exploring this reactive version of the ultimatum game where the acceptance by players depends on the offer. In order to do so, we analyze two situations: (i) mean field and (ii) we consider players inserted within the networks with arbitrary coordination. We then show that the reactive aspect, here studied, thus far not analyzed in the evolutionary game theory literature can unveil an essential feature for the convergence to fifty-fifty split. Moreover we also analyze populations under four different polices ranging from a highly conservative to a moderate one, with respect to the decision in changing the proposal based on acceptances. We show that the idea of gaining less more times added to the reciprocity of the players is highly relevant to the concept of ;healthy; societies population bargaining.

An evolutionary game model for behavioral gambit of loyalists: Global awareness and risk-aversion

NASA Astrophysics Data System (ADS)

Alfinito, E.; Barra, A.; Beccaria, M.; Fachechi, A.; Macorini, G.

2018-02-01

We study the phase diagram of a minority game where three classes of agents are present. Two types of agents play a risk-loving game that we model by the standard Snowdrift Game. The behaviour of the third type of agents is coded by indifference with respect to the game at all: their dynamics is designed to account for risk-aversion as an innovative behavioral gambit. From this point of view, the choice of this solitary strategy is enhanced when innovation starts, while is depressed when it becomes the majority option. This implies that the payoff matrix of the game becomes dependent on the global awareness of the agents measured by the relevance of the population of the indifferent players. The resulting dynamics is nontrivial with different kinds of phase transition depending on a few model parameters. The phase diagram is studied on regular as well as complex networks.

Evolutionary stability concepts in a stochastic environment

NASA Astrophysics Data System (ADS)

Zheng, Xiu-Deng; Li, Cong; Lessard, Sabin; Tao, Yi

2017-09-01

Over the past 30 years, evolutionary game theory and the concept of an evolutionarily stable strategy have been not only extensively developed and successfully applied to explain the evolution of animal behaviors, but also widely used in economics and social sciences. Nonetheless, the stochastic dynamical properties of evolutionary games in randomly fluctuating environments are still unclear. In this study, we investigate conditions for stochastic local stability of fixation states and constant interior equilibria in a two-phenotype model with random payoffs following pairwise interactions. Based on this model, we develop the concepts of stochastic evolutionary stability (SES) and stochastic convergence stability (SCS). We show that the condition for a pure strategy to be SES and SCS is more stringent than in a constant environment, while the condition for a constant mixed strategy to be SES is less stringent than the condition to be SCS, which is less stringent than the condition in a constant environment.

When Reputation Enforces Evolutionary Cooperation in Unreliable MANETs.

PubMed

Tang, Changbing; Li, Ang; Li, Xiang

2015-10-01

In self-organized mobile ad hoc networks (MANETs), network functions rely on cooperation of self-interested nodes, where a challenge is to enforce their mutual cooperation. In this paper, we study cooperative packet forwarding in a one-hop unreliable channel which results from loss of packets and noisy observation of transmissions. We propose an indirect reciprocity framework based on evolutionary game theory, and enforce cooperation of packet forwarding strategies in both structured and unstructured MANETs. Furthermore, we analyze the evolutionary dynamics of cooperative strategies and derive the threshold of benefit-to-cost ratio to guarantee the convergence of cooperation. The numerical simulations verify that the proposed evolutionary game theoretic solution enforces cooperation when the benefit-to-cost ratio of the altruistic exceeds the critical condition. In addition, the network throughput performance of our proposed strategy in structured MANETs is measured, which is in close agreement with that of the full cooperative strategy.

Supercooperation in evolutionary games on correlated weighted networks.

PubMed

Buesser, Pierre; Tomassini, Marco

2012-01-01

In this work we study the behavior of classical two-person, two-strategies evolutionary games on a class of weighted networks derived from Barabási-Albert and random scale-free unweighted graphs. Using customary imitative dynamics, our numerical simulation results show that the presence of link weights that are correlated in a particular manner with the degree of the link end points leads to unprecedented levels of cooperation in the whole games' phase space, well above those found for the corresponding unweighted complex networks. We provide intuitive explanations for this favorable behavior by transforming the weighted networks into unweighted ones with particular topological properties. The resulting structures help us to understand why cooperation can thrive and also give ideas as to how such supercooperative networks might be built.

Research on Duplication Dynamics and Evolutionary Stable of Reverse Supply Chain

NASA Astrophysics Data System (ADS)

Huizhong, Dong; Hongli, Song

An evolutionary game model of Reverse Supply Chain(RSC) is established based on duplication dynamics function and evolutionary stable strategy. Using the model framework, this paper provides insights into a deeper understanding on how each supplier make strategic decision independently in reverse supply chain to determine their performance. The main conclusion is as follow: Under the market mechanism, not unless the extra income derived from the implementation of RSC exceeds zero point would the suppliers implement RSC strategy. When those suppliers are passive to RSC, the effective solution is that the government takes macro-control measures, for example, to force those suppliers implement RSC through punishment mechanism.

Learning dynamics explains human behaviour in prisoner's dilemma on networks.

PubMed

Cimini, Giulio; Sánchez, Angel

2014-05-06

Cooperative behaviour lies at the very basis of human societies, yet its evolutionary origin remains a key unsolved puzzle. Whereas reciprocity or conditional cooperation is one of the most prominent mechanisms proposed to explain the emergence of cooperation in social dilemmas, recent experimental findings on networked Prisoner's Dilemma games suggest that conditional cooperation also depends on the previous action of the player-namely on the 'mood' in which the player is currently in. Roughly, a majority of people behave as conditional cooperators if they cooperated in the past, whereas they ignore the context and free ride with high probability if they did not. However, the ultimate origin of this behaviour represents a conundrum itself. Here, we aim specifically to provide an evolutionary explanation of moody conditional cooperation (MCC). To this end, we perform an extensive analysis of different evolutionary dynamics for players' behavioural traits-ranging from standard processes used in game theory based on pay-off comparison to others that include non-economic or social factors. Our results show that only a dynamic built upon reinforcement learning is able to give rise to evolutionarily stable MCC, and at the end to reproduce the human behaviours observed in the experiments.

Behavior of Collective Cooperation Yielded by Two Update Rules in Social Dilemmas: Combining Fermi and Moran Rules

NASA Astrophysics Data System (ADS)

Xia, Cheng-Yi; Wang, Lei; Wang, Juan; Wang, Jin-Song

2012-09-01

We combine the Fermi and Moran update rules in the spatial prisoner's dilemma and snowdrift games to investigate the behavior of collective cooperation among agents on the regular lattice. Large-scale simulations indicate that, compared to the model with only one update rule, the cooperation behavior exhibits the richer phenomena, and the role of update dynamics should be paid more attention in the evolutionary game theory. Meanwhile, we also observe that the introduction of Moran rule, which needs to consider all neighbor's information, can markedly promote the aggregate cooperation level, that is, randomly selecting the neighbor proportional to its payoff to imitate will facilitate the cooperation among agents. Current results will contribute to further understand the cooperation dynamics and evolutionary behaviors within many biological, economic and social systems.

Evolutionary dynamics of social dilemmas in structured heterogeneous populations.

PubMed

Santos, F C; Pacheco, J M; Lenaerts, Tom

2006-02-28

Real populations have been shown to be heterogeneous, in which some individuals have many more contacts than others. This fact contrasts with the traditional homogeneous setting used in studies of evolutionary game dynamics. We incorporate heterogeneity in the population by studying games on graphs, in which the variability in connectivity ranges from single-scale graphs, for which heterogeneity is small and associated degree distributions exhibit a Gaussian tale, to scale-free graphs, for which heterogeneity is large with degree distributions exhibiting a power-law behavior. We study the evolution of cooperation, modeled in terms of the most popular dilemmas of cooperation. We show that, for all dilemmas, increasing heterogeneity favors the emergence of cooperation, such that long-term cooperative behavior easily resists short-term noncooperative behavior. Moreover, we show how cooperation depends on the intricate ties between individuals in scale-free populations.

Random and non-random mating populations: Evolutionary dynamics in meiotic drive.

PubMed

Sarkar, Bijan

2016-01-01

Game theoretic tools are utilized to analyze a one-locus continuous selection model of sex-specific meiotic drive by considering nonequivalence of the viabilities of reciprocal heterozygotes that might be noticed at an imprinted locus. The model draws attention to the role of viability selections of different types to examine the stable nature of polymorphic equilibrium. A bridge between population genetics and evolutionary game theory has been built up by applying the concept of the Fundamental Theorem of Natural Selection. In addition to pointing out the influences of male and female segregation ratios on selection, configuration structure reveals some noted results, e.g., Hardy-Weinberg frequencies hold in replicator dynamics, occurrence of faster evolution at the maximized variance fitness, existence of mixed Evolutionarily Stable Strategy (ESS) in asymmetric games, the tending evolution to follow not only a 1:1 sex ratio but also a 1:1 different alleles ratio at particular gene locus. Through construction of replicator dynamics in the group selection framework, our selection model introduces a redefining bases of game theory to incorporate non-random mating where a mating parameter associated with population structure is dependent on the social structure. Also, the model exposes the fact that the number of polymorphic equilibria will depend on the algebraic expression of population structure. Copyright © 2015 Elsevier Inc. All rights reserved.

Minority games, evolving capitals and replicator dynamics

NASA Astrophysics Data System (ADS)

Galla, Tobias; Zhang, Yi-Cheng

2009-11-01

We discuss a simple version of the minority game (MG) in which agents hold only one strategy each, but in which their capitals evolve dynamically according to their success and in which the total trading volume varies in time accordingly. This feature is known to be crucial for MGs to reproduce stylized facts of real market data. The stationary states and phase diagram of the model can be computed, and we show that the ergodicity breaking phase transition common for MGs, and marked by a divergence of the integrated response, is present also in this simplified model. An analogous majority game turns out to be relatively void of interesting features, and the total capital is found to diverge in time. Introducing a restraining force leads to a model akin to the replicator dynamics of evolutionary game theory, and we demonstrate that here a different type of phase transition is observed. Finally we briefly discuss the relation of this model with one strategy per player to more sophisticated minority games with dynamical capitals and several trading strategies per agent.

A Study on Standard Competition with Network Effect Based on Evolutionary Game Model

NASA Astrophysics Data System (ADS)

Wang, Ye; Wang, Bingdong; Li, Kangning

Owing to networks widespread in modern society, standard competition with network effect is now endowed with new connotation. This paper aims to study the impact of network effect on standard competition; it is organized in the mode of "introduction-model setup-equilibrium analysis-conclusion". Starting from a well-structured model of evolutionary game, it is then extended to a dynamic analysis. This article proves both theoretically and empirically that whether or not a standard can lead the market trends depends on the utility it would bring, and the author also discusses some advisable strategies revolving around the two factors of initial position and border break.

Cooperation and stability through periodic impulses.

PubMed

Zhang, Bo-Yu; Cressman, Ross; Tao, Yi

2010-03-29

Basic games, where each individual chooses between two strategies, illustrate several issues that immediately emerge from the standard approach that applies strategic reasoning, based on rational decisions, to predict population behavior where no rationality is assumed. These include how mutual cooperation (which corresponds to the best outcome from the population perspective) can evolve when the only individually rational choice is to defect, illustrated by the Prisoner's Dilemma (PD) game, and how individuals can randomize between two strategies when neither is individually rational, illustrated by the Battle of the Sexes (BS) game that models male-female conflict over parental investment in offspring. We examine these questions from an evolutionary perspective where the evolutionary dynamics includes an impulsive effect that models sudden changes in collective population behavior. For the PD game, we show analytically that cooperation can either coexist with defection or completely take over the population, depending on the strength of the impulse. By extending these results for the PD game, we also show that males and females each evolve to a single strategy in the BS game when the impulsive effect is strong and that weak impulses stabilize the randomized strategies of this game.

Evidence Combination From an Evolutionary Game Theory Perspective

PubMed Central

Deng, Xinyang; Han, Deqiang; Dezert, Jean; Deng, Yong; Shyr, Yu

2017-01-01

Dempster-Shafer evidence theory is a primary methodology for multi-source information fusion because it is good at dealing with uncertain information. This theory provides a Dempster’s rule of combination to synthesize multiple evidences from various information sources. However, in some cases, counter-intuitive results may be obtained based on that combination rule. Numerous new or improved methods have been proposed to suppress these counter-intuitive results based on perspectives, such as minimizing the information loss or deviation. Inspired by evolutionary game theory, this paper considers a biological and evolutionary perspective to study the combination of evidences. An evolutionary combination rule (ECR) is proposed to help find the most biologically supported proposition in a multi-evidence system. Within the proposed ECR, we develop a Jaccard matrix game (JMG) to formalize the interaction between propositions in evidences, and utilize the replicator dynamics to mimick the evolution of propositions. Experimental results show that the proposed ECR can effectively suppress the counter-intuitive behaviors appeared in typical paradoxes of evidence theory, compared with many existing methods. Properties of the ECR, such as solution’s stability and convergence, have been mathematically proved as well. PMID:26285231

A Simple Mechanism for Cooperation in the Well-Mixed Prisoner's Dilemma Game

NASA Astrophysics Data System (ADS)

Perc, Matjaž

2008-11-01

I show that the addition of Gaussian noise to the payoffs is able to stabilize cooperation in well-mixed populations, where individuals play the prisoner's dilemma game. The impact of stochasticity on the evolutionary dynamics can be expressed deterministically via a simple small-noise expansion of multiplicative noisy terms. In particular, cooperation emerges as a stable noise-induced steady state in the replicator dynamics. Due to the generality of the employed theoretical framework, presented results should prove valuable in various scientific disciplines, ranging from economy to ecology.

Equilibria, information and frustration in heterogeneous network games with conflicting preferences

NASA Astrophysics Data System (ADS)

Mazzoli, M.; Sánchez, A.

2017-11-01

Interactions between people are the basis on which the structure of our society arises as a complex system and, at the same time, are the starting point of any physical description of it. In the last few years, much theoretical research has addressed this issue by combining the physics of complex networks with a description of interactions in terms of evolutionary game theory. We here take this research a step further by introducing a most salient societal factor such as the individuals’ preferences, a characteristic that is key to understanding much of the social phenomenology these days. We consider a heterogeneous, agent-based model in which agents interact strategically with their neighbors, but their preferences and payoffs for the possible actions differ. We study how such a heterogeneous network behaves under evolutionary dynamics and different strategic interactions, namely coordination games and best shot games. With this model we study the emergence of the equilibria predicted analytically in random graphs under best response dynamics, and we extend this test to unexplored contexts like proportional imitation and scale free networks. We show that some theoretically predicted equilibria do not arise in simulations with incomplete information, and we demonstrate the importance of the graph topology and the payoff function parameters for some games. Finally, we discuss our results with the available experimental evidence on coordination games, showing that our model agrees better with the experiment than standard economic theories, and draw hints as to how to maximize social efficiency in situations of conflicting preferences.

Effects of dynamical grouping on cooperation in N-person evolutionary snowdrift game

NASA Astrophysics Data System (ADS)

Ji, M.; Xu, C.; Hui, P. M.

2011-09-01

A population typically consists of agents that continually distribute themselves into different groups at different times. This dynamic grouping has recently been shown to be essential in explaining many features observed in human activities including social, economic, and military activities. We study the effects of dynamic grouping on the level of cooperation in a modified evolutionary N-person snowdrift game. Due to the formation of dynamical groups, the competition takes place in groups of different sizes at different times and players of different strategies are mixed by the grouping dynamics. It is found that the level of cooperation is greatly enhanced by the dynamic grouping of agents, when compared with a static population of the same size. As a parameter β, which characterizes the relative importance of the reward and cost, increases, the fraction of cooperative players fC increases and it is possible to achieve a fully cooperative state. Analytically, we present a dynamical equation that incorporates the effects of the competing game and group size distribution. The distribution of cooperators in different groups is assumed to be a binomial distribution, which is confirmed by simulations. Results from the analytic equation are in good agreement with numerical results from simulations. We also present detailed simulation results of fC over the parameter space spanned by the probabilities of group coalescence νm and group fragmentation νp in the grouping dynamics. A high νm and low νp promotes cooperation, and a favorable reward characterized by a high β would lead to a fully cooperative state.

Nature-Inspired Cognitive Evolution to Play MS. Pac-Man

NASA Astrophysics Data System (ADS)

Tan, Tse Guan; Teo, Jason; Anthony, Patricia

Recent developments in nature-inspired computation have heightened the need for research into the three main areas of scientific, engineering and industrial applications. Some approaches have reported that it is able to solve dynamic problems and very useful for improving the performance of various complex systems. So far however, there has been little discussion about the effectiveness of the application of these models to computer and video games in particular. The focus of this research is to explore the hybridization of nature-inspired computation methods for optimization of neural network-based cognition in video games, in this case the combination of a neural network with an evolutionary algorithm. In essence, a neural network is an attempt to mimic the extremely complex human brain system, which is building an artificial brain that is able to self-learn intelligently. On the other hand, an evolutionary algorithm is to simulate the biological evolutionary processes that evolve potential solutions in order to solve the problems or tasks by applying the genetic operators such as crossover, mutation and selection into the solutions. This paper investigates the abilities of Evolution Strategies (ES) to evolve feed-forward artificial neural network's internal parameters (i.e. weight and bias values) for automatically generating Ms. Pac-man controllers. The main objective of this game is to clear a maze of dots while avoiding the ghosts and to achieve the highest possible score. The experimental results show that an ES-based system can be successfully applied to automatically generate artificial intelligence for a complex, dynamic and highly stochastic video game environment.

Evolutionary Game Theory in Growing Populations

NASA Astrophysics Data System (ADS)

Melbinger, Anna; Cremer, Jonas; Frey, Erwin

2010-10-01

Existing theoretical models of evolution focus on the relative fitness advantages of different mutants in a population while the dynamic behavior of the population size is mostly left unconsidered. We present here a generic stochastic model which combines the growth dynamics of the population and its internal evolution. Our model thereby accounts for the fact that both evolutionary and growth dynamics are based on individual reproduction events and hence are highly coupled and stochastic in nature. We exemplify our approach by studying the dilemma of cooperation in growing populations and show that genuinely stochastic events can ease the dilemma by leading to a transient but robust increase in cooperation.

Edge effects in game-theoretic dynamics of spatially structured tumours.

PubMed

Kaznatcheev, Artem; Scott, Jacob G; Basanta, David

2015-07-06

Cancer dynamics are an evolutionary game between cellular phenotypes. A typical assumption in this modelling paradigm is that the probability of a given phenotypic strategy interacting with another depends exclusively on the abundance of those strategies without regard for local neighbourhood structure. We address this limitation by using the Ohtsuki-Nowak transform to introduce spatial structure to the go versus grow game. We show that spatial structure can promote the invasive (go) strategy. By considering the change in neighbourhood size at a static boundary--such as a blood vessel, organ capsule or basement membrane--we show an edge effect that allows a tumour without invasive phenotypes in the bulk to have a polyclonal boundary with invasive cells. We present an example of this promotion of invasive (epithelial-mesenchymal transition-positive) cells in a metastatic colony of prostate adenocarcinoma in bone marrow. Our results caution that pathologic analyses that do not distinguish between cells in the bulk and cells at a static edge of a tumour can underestimate the number of invasive cells. Although we concentrate on applications in mathematical oncology, we expect our approach to extend to other evolutionary game models where interaction neighbourhoods change at fixed system boundaries. © 2015 The Author(s) Published by the Royal Society. All rights reserved.

The Replicator Equation on Graphs

PubMed Central

Ohtsuki, Hisashi; Nowak, Martin A.

2008-01-01

We study evolutionary games on graphs. Each player is represented by a vertex of the graph. The edges denote who meets whom. A player can use any one of n strategies. Players obtain a payoff from interaction with all their immediate neighbors. We consider three different update rules, called ‘birth-death’, ‘death-birth’ and ‘imitation’. A fourth update rule, ‘pairwise comparison’, is shown to be equivalent to birth-death updating in our model. We use pair-approximation to describe the evolutionary game dynamics on regular graphs of degree k. In the limit of weak selection, we can derive a differential equation which describes how the average frequency of each strategy on the graph changes over time. Remarkably, this equation is a replicator equation with a transformed payoff matrix. Therefore, moving a game from a well-mixed population (the complete graph) onto a regular graph simply results in a transformation of the payoff matrix. The new payoff matrix is the sum of the original payoff matrix plus another matrix, which describes the local competition of strategies. We discuss the application of our theory to four particular examples, the Prisoner’s Dilemma, the Snow-Drift game, a coordination game and the Rock-Scissors-Paper game. PMID:16860343

Cheating is evolutionarily assimilated with cooperation in the continuous snowdrift game

PubMed Central

Sasaki, Tatsuya; Okada, Isamu

2015-01-01

It is well known that in contrast to the Prisoner’s Dilemma, the snowdrift game can lead to a stable coexistence of cooperators and cheaters. Recent theoretical evidence on the snowdrift game suggests that gradual evolution for individuals choosing to contribute in continuous degrees can result in the social diversification to a 100% contribution and 0% contribution through so-called evolutionary branching. Until now, however, game-theoretical studies have shed little light on the evolutionary dynamics and consequences of the loss of diversity in strategy. Here, we analyze continuous snowdrift games with quadratic payoff functions in dimorphic populations. Subsequently, conditions are clarified under which gradual evolution can lead a population consisting of those with 100% contribution and those with 0% contribution to merge into one species with an intermediate contribution level. The key finding is that the continuous snowdrift game is more likely to lead to assimilation of different cooperation levels rather than maintenance of diversity. Importantly, this implies that allowing the gradual evolution of cooperative behavior can facilitate social inequity aversion in joint ventures that otherwise could cause conflicts that are based on commonly accepted notions of fairness. PMID:25868940

Cheating is evolutionarily assimilated with cooperation in the continuous snowdrift game.

PubMed

Sasaki, Tatsuya; Okada, Isamu

2015-05-01

It is well known that in contrast to the Prisoner's Dilemma, the snowdrift game can lead to a stable coexistence of cooperators and cheaters. Recent theoretical evidence on the snowdrift game suggests that gradual evolution for individuals choosing to contribute in continuous degrees can result in the social diversification to a 100% contribution and 0% contribution through so-called evolutionary branching. Until now, however, game-theoretical studies have shed little light on the evolutionary dynamics and consequences of the loss of diversity in strategy. Here, we analyze continuous snowdrift games with quadratic payoff functions in dimorphic populations. Subsequently, conditions are clarified under which gradual evolution can lead a population consisting of those with 100% contribution and those with 0% contribution to merge into one species with an intermediate contribution level. The key finding is that the continuous snowdrift game is more likely to lead to assimilation of different cooperation levels rather than maintenance of diversity. Importantly, this implies that allowing the gradual evolution of cooperative behavior can facilitate social inequity aversion in joint ventures that otherwise could cause conflicts that are based on commonly accepted notions of fairness. Copyright © 2015 The Authors. Published by Elsevier Ireland Ltd.. All rights reserved.

Evolutionary stability for matrix games under time constraints.

PubMed

Garay, József; Csiszár, Villő; Móri, Tamás F

2017-02-21

Game theory focuses on payoffs and typically ignores time constraints that play an important role in evolutionary processes where the repetition of games can depend on the strategies, too. We introduce a matrix game under time constraints, where each pairwise interaction has two consequences: both players receive a payoff and they cannot play the next game for a specified time duration. Thus our model is defined by two matrices: a payoff matrix and an average time duration matrix. Maynard Smith's concept of evolutionary stability is extended to this class of games. We illustrate the effect of time constraints by the well-known prisoner's dilemma game, where additional time constraints can ensure the existence of unique evolutionary stable strategies (ESS), both pure and mixed, or the coexistence of two pure ESS. Our general results may be useful in several fields of biology where evolutionary game theory is applied, principally in ecological games, where time constraints play an inevitable role. Copyright © 2016 Elsevier Ltd. All rights reserved.

Role-separating ordering in social dilemmas controlled by topological frustration

NASA Astrophysics Data System (ADS)

Amaral, Marco A.; Perc, Matjaž; Wardil, Lucas; Szolnoki, Attila; da Silva Júnior, Elton J.; da Silva, Jafferson K. L.

2017-03-01

``Three is a crowd" is an old proverb that applies as much to social interactions as it does to frustrated configurations in statistical physics models. Accordingly, social relations within a triangle deserve special attention. With this motivation, we explore the impact of topological frustration on the evolutionary dynamics of the snowdrift game on a triangular lattice. This topology provides an irreconcilable frustration, which prevents anticoordination of competing strategies that would be needed for an optimal outcome of the game. By using different strategy updating protocols, we observe complex spatial patterns in dependence on payoff values that are reminiscent to a honeycomb-like organization, which helps to minimize the negative consequence of the topological frustration. We relate the emergence of these patterns to the microscopic dynamics of the evolutionary process, both by means of mean-field approximations and Monte Carlo simulations. For comparison, we also consider the same evolutionary dynamics on the square lattice, where of course the topological frustration is absent. However, with the deletion of diagonal links of the triangular lattice, we can gradually bridge the gap to the square lattice. Interestingly, in this case the level of cooperation in the system is a direct indicator of the level of topological frustration, thus providing a method to determine frustration levels in an arbitrary interaction network.

Role-separating ordering in social dilemmas controlled by topological frustration.

PubMed

Amaral, Marco A; Perc, Matjaž; Wardil, Lucas; Szolnoki, Attila; da Silva Júnior, Elton J; da Silva, Jafferson K L

2017-03-01

''Three is a crowd" is an old proverb that applies as much to social interactions as it does to frustrated configurations in statistical physics models. Accordingly, social relations within a triangle deserve special attention. With this motivation, we explore the impact of topological frustration on the evolutionary dynamics of the snowdrift game on a triangular lattice. This topology provides an irreconcilable frustration, which prevents anticoordination of competing strategies that would be needed for an optimal outcome of the game. By using different strategy updating protocols, we observe complex spatial patterns in dependence on payoff values that are reminiscent to a honeycomb-like organization, which helps to minimize the negative consequence of the topological frustration. We relate the emergence of these patterns to the microscopic dynamics of the evolutionary process, both by means of mean-field approximations and Monte Carlo simulations. For comparison, we also consider the same evolutionary dynamics on the square lattice, where of course the topological frustration is absent. However, with the deletion of diagonal links of the triangular lattice, we can gradually bridge the gap to the square lattice. Interestingly, in this case the level of cooperation in the system is a direct indicator of the level of topological frustration, thus providing a method to determine frustration levels in an arbitrary interaction network.

Epigenetic battle of the sexes. Comment on: ;Epigenetic game theory: How to compute the epigenetic control of maternal-to-zygotic transition; by Qian Wang et al.

NASA Astrophysics Data System (ADS)

Wu, Song

2017-03-01

Qian Wang et al. present an interesting framework, named epigenetic game theory, for modeling sex-based epigenetic dynamics during embryogenesis from a new viewpoint of evolutionary game theory [1]. That is, epigenomes of sperms and oocytes may coordinate through either cooperation or competition, or both, to affect the fitness of embryos. The work uses a set of ordinary differential equations (ODEs) to describe longitudinal trajectories of DNA methylation levels in both parental and maternal gametes and their dependence on each other. The insights gained from this review, i.e. dynamic methylation profiles and their interaction are potentially important to many fields, such as biomedicine and agriculture.

Multi-objective optimization of an arch dam shape under static loads using an evolutionary game method

NASA Astrophysics Data System (ADS)

Meng, Rui; Cheong, Kang Hao; Bao, Wei; Wong, Kelvin Kian Loong; Wang, Lu; Xie, Neng-gang

2018-06-01

This article attempts to evaluate the safety and economic performance of an arch dam under the action of static loads. The geometric description of a crown cantilever section and the horizontal arch ring is presented. A three-objective optimization model of arch dam shape is established based on the arch dam volume, maximum principal tensile stress and total strain energy. The evolutionary game method is then applied to obtain the optimal solution. In the evolutionary game technique, a novel and more efficient exploration method of the game players' strategy space, named the 'sorting partition method under the threshold limit', is presented, with the game profit functions constructed according to both competitive and cooperative behaviour. By way of example, three optimization goals have all shown improvements over the initial solutions. In particular, the evolutionary game method has potentially faster convergence. This demonstrates the preliminary proof of principle of the evolutionary game method.

Chaotic evolution of prisoner's dilemma game with volunteering on interdependent networks

NASA Astrophysics Data System (ADS)

Luo, Chao; Zhang, Xiaolin; Zheng, YuanJie

2017-06-01

In this article, the evolution of prisoner's dilemma game with volunteering on interdependent networks is investigated. Different from the traditional two-strategy game, voluntary participation as an additional strategy is involved in repeated game, that can introduce more complex evolutionary dynamics. And, interdependent networks provide a more generalized network architecture to study the intricate variability of dynamics. We have showed that voluntary participation could effectively promote the density of co-operation, that is also greatly affected by interdependent strength between two coupled networks. We further discussed the influence of interdependent strength on the densities of different strategies and found that an intermediate interdependence would play a bigger role on the evolution of dynamics. Subsequently, the critical values of the defection temptation for phase transitions under different conditions have been studied. Moreover, the global oscillations induced by the circle of dominance of three strategies on interdependent networks have been quantitatively investigated. Counter-intuitively, the oscillations of strategy densities are not periodic or stochastic, but have rich dynamical behaviors. By means of various analysis tools, we have demonstrated the global oscillations of strategy densities possessed chaotic characteristics.

Triple grouping and period-three oscillations in minority-game dynamics.

PubMed

Dong, Jia-Qi; Huang, Zi-Gang; Huang, Liang; Lai, Ying-Cheng

2014-12-01

Dynamical systems based on the minority game (MG) have been a paradigm for gaining significant insights into a variety of social and biological behaviors. Recently, a grouping phenomenon has been unveiled in MG systems of multiple resources (strategies) in which the strategies spontaneously break into an even number of groups, each exhibiting an identical oscillation pattern in the attendance of game players. Here we report our finding of spontaneous breakup of resources into three groups, each exhibiting period-three oscillations. An analysis is developed to understand the emergence of the striking phenomenon of triple grouping and period-three oscillations. In the presence of random disturbances, the triple-group/period-three state becomes transient, and we obtain explicit formula for the average transient lifetime using two methods of approximation. Our finding indicates that, period-three oscillation, regarded as one of the most fundamental behaviors in smooth nonlinear dynamical systems, can also occur in much more complex, evolutionary-game dynamical systems. Our result also provides a plausible insight for the occurrence of triple grouping observed, for example, in the U.S. housing market.

Preferential selection based on strategy persistence and memory promotes cooperation in evolutionary prisoner's dilemma games

NASA Astrophysics Data System (ADS)

Liu, Yuanming; Huang, Changwei; Dai, Qionglin

2018-06-01

Strategy imitation plays a crucial role in evolutionary dynamics when we investigate the spontaneous emergence of cooperation under the framework of evolutionary game theory. Generally, when an individual updates his strategy, he needs to choose a role model whom he will learn from. In previous studies, individuals choose role models randomly from their neighbors. In recent works, researchers have considered that individuals choose role models according to neighbors' attractiveness characterized by the present network topology or historical payoffs. Here, we associate an individual's attractiveness with the strategy persistence, which characterizes how frequently he changes his strategy. We introduce a preferential parameter α to describe the nonlinear correlation between the selection probability and the strategy persistence and the memory length of individuals M into the evolutionary games. We investigate the effects of α and M on cooperation. Our results show that cooperation could be promoted when α > 0 and at the same time M > 1, which corresponds to the situation that individuals are inclined to select their neighbors with relatively higher persistence levels during the evolution. Moreover, we find that the cooperation level could reach the maximum at an optimal memory length when α > 0. Our work sheds light on how to promote cooperation through preferential selection based on strategy persistence and a limited memory length.

Motifs, modules and games in bacteria.

PubMed

Wolf, Denise M; Arkin, Adam P

2003-04-01

Global explorations of regulatory network dynamics, organization and evolution have become tractable thanks to high-throughput sequencing and molecular measurement of bacterial physiology. From these, a nascent conceptual framework is developing, that views the principles of regulation in term of motifs, modules and games. Motifs are small, repeated, and conserved biological units ranging from molecular domains to small reaction networks. They are arranged into functional modules, genetically dissectible cellular functions such as the cell cycle, or different stress responses. The dynamical functioning of modules defines the organism's strategy to survive in a game, pitting cell against cell, and cell against environment. Placing pathway structure and dynamics into an evolutionary context begins to allow discrimination between those physical and molecular features that particularize a species to its surroundings, and those that provide core physiological function. This approach promises to generate a higher level understanding of cellular design, pathway evolution and cellular bioengineering.

Motifs, modules and games in bacteria

DOE Office of Scientific and Technical Information (OSTI.GOV)

Wolf, Denise M.; Arkin, Adam P.

2003-04-01

Global explorations of regulatory network dynamics, organization and evolution have become tractable thanks to high-throughput sequencing and molecular measurement of bacterial physiology. From these, a nascent conceptual framework is developing, that views the principles of regulation in term of motifs, modules and games. Motifs are small, repeated, and conserved biological units ranging from molecular domains to small reaction networks. They are arranged into functional modules, genetically dissectible cellular functions such as the cell cycle, or different stress responses. The dynamical functioning of modules defines the organism's strategy to survive in a game, pitting cell against cell, and cell against environment.more » Placing pathway structure and dynamics into an evolutionary context begins to allow discrimination between those physical and molecular features that particularize a species to its surroundings, and those that provide core physiological function. This approach promises to generate a higher level understanding of cellular design, pathway evolution and cellular bioengineering.« less

Dynamics of prebiotic RNA reproduction illuminated by chemical game theory

PubMed Central

Yeates, Jessica A. M.; Hilbe, Christian; Zwick, Martin; Nowak, Martin A.; Lehman, Niles

2016-01-01

Many origins-of-life scenarios depict a situation in which there are common and potentially scarce resources needed by molecules that compete for survival and reproduction. The dynamics of RNA assembly in a complex mixture of sequences is a frequency-dependent process and mimics such scenarios. By synthesizing Azoarcus ribozyme genotypes that differ in their single-nucleotide interactions with other genotypes, we can create molecules that interact among each other to reproduce. Pairwise interplays between RNAs involve both cooperation and selfishness, quantifiable in a 2 × 2 payoff matrix. We show that a simple model of differential equations based on chemical kinetics accurately predicts the outcomes of these molecular competitions using simple rate inputs into these matrices. In some cases, we find that mixtures of different RNAs reproduce much better than each RNA type alone, reflecting a molecular form of reciprocal cooperation. We also demonstrate that three RNA genotypes can stably coexist in a rock–paper–scissors analog. Our experiments suggest a new type of evolutionary game dynamics, called prelife game dynamics or chemical game dynamics. These operate without template-directed replication, illustrating how small networks of RNAs could have developed and evolved in an RNA world. PMID:27091972

Dynamics of prebiotic RNA reproduction illuminated by chemical game theory.

PubMed

Yeates, Jessica A M; Hilbe, Christian; Zwick, Martin; Nowak, Martin A; Lehman, Niles

2016-05-03

Many origins-of-life scenarios depict a situation in which there are common and potentially scarce resources needed by molecules that compete for survival and reproduction. The dynamics of RNA assembly in a complex mixture of sequences is a frequency-dependent process and mimics such scenarios. By synthesizing Azoarcus ribozyme genotypes that differ in their single-nucleotide interactions with other genotypes, we can create molecules that interact among each other to reproduce. Pairwise interplays between RNAs involve both cooperation and selfishness, quantifiable in a 2 × 2 payoff matrix. We show that a simple model of differential equations based on chemical kinetics accurately predicts the outcomes of these molecular competitions using simple rate inputs into these matrices. In some cases, we find that mixtures of different RNAs reproduce much better than each RNA type alone, reflecting a molecular form of reciprocal cooperation. We also demonstrate that three RNA genotypes can stably coexist in a rock-paper-scissors analog. Our experiments suggest a new type of evolutionary game dynamics, called prelife game dynamics or chemical game dynamics. These operate without template-directed replication, illustrating how small networks of RNAs could have developed and evolved in an RNA world.

Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics

NASA Astrophysics Data System (ADS)

Roca, Carlos P.; Cuesta, José A.; Sánchez, Angel

2009-12-01

Evolutionary game dynamics is one of the most fruitful frameworks for studying evolution in different disciplines, from Biology to Economics. Within this context, the approach of choice for many researchers is the so-called replicator equation, that describes mathematically the idea that those individuals performing better have more offspring and thus their frequency in the population grows. While very many interesting results have been obtained with this equation in the three decades elapsed since it was first proposed, it is important to realize the limits of its applicability. One particularly relevant issue in this respect is that of non-mean-field effects, that may arise from temporal fluctuations or from spatial correlations, both neglected in the replicator equation. This review discusses these temporal and spatial effects focusing on the non-trivial modifications they induce when compared to the outcome of replicator dynamics. Alongside this question, the hypothesis of linearity and its relation to the choice of the rule for strategy update is also analyzed. The discussion is presented in terms of the emergence of cooperation, as one of the current key problems in Biology and in other disciplines.

Imitation versus payoff: Duality of the decision-making process demonstrates criticality and consensus formation

NASA Astrophysics Data System (ADS)

Turalska, M.; West, B. J.

2014-11-01

We consider a dual model of decision making, in which an individual forms its opinion based on contrasting mechanisms of imitation and rational calculation. The decision-making model (DMM) implements imitating behavior by means of a network of coupled two-state master equations that undergoes a phase transition at a critical value of a control parameter. The evolutionary spatial game, being a generalization of the prisoner's dilemma game, is used to determine in objective fashion the cooperative or anticooperative strategy adopted by individuals. Interactions between two sources of dynamics increases the domain of initial states attracted to phase transition dynamics beyond that of the DMM network in isolation. Additionally, on average the influence of the DMM on the game increases the final observed fraction of cooperators in the system.

Heterogeneous update mechanisms in evolutionary games: Mixing innovative and imitative dynamics

NASA Astrophysics Data System (ADS)

Amaral, Marco Antonio; Javarone, Marco Alberto

2018-04-01

Innovation and evolution are two processes of paramount relevance for social and biological systems. In general, the former allows the introduction of elements of novelty, while the latter is responsible for the motion of a system in its phase space. Often, these processes are strongly related, since an innovation can trigger the evolution, and the latter can provide the optimal conditions for the emergence of innovations. Both processes can be studied by using the framework of evolutionary game theory, where evolution constitutes an intrinsic mechanism. At the same time, the concept of innovation requires an opportune mathematical representation. Notably, innovation can be modeled as a strategy, or it can constitute the underlying mechanism that allows agents to change strategy. Here, we analyze the second case, investigating the behavior of a heterogeneous population, composed of imitative and innovative agents. Imitative agents change strategy only by imitating that of their neighbors, whereas innovative ones change strategy without the need for a copying source. The proposed model is analyzed by means of analytical calculations and numerical simulations in different topologies. Remarkably, results indicate that the mixing of mechanisms can be detrimental to cooperation near phase transitions. In those regions, the spatial reciprocity from imitative mechanisms is destroyed by innovative agents, leading to the downfall of cooperation. Our investigation sheds some light on the complex dynamics emerging from the heterogeneity of strategy revision methods, highlighting the role of innovation in evolutionary games.

Evolutionary Dynamics of Collective Action in Structured Populations

NASA Astrophysics Data System (ADS)

Santos, Marta Daniela de Almeida

The pervasiveness of cooperation in Nature is not easily explained. If evolution is characterized by competition and survival of the fittest, why should selfish individuals cooperate with each other? Evolutionary Game Theory (EGT) provides a suitable mathematical framework to study this problem, central to many areas of science. Conventionally, interactions between individuals are modeled in terms of one-shot, symmetric 2-Person Dilemmas of Cooperation, but many real-life situations involve decisions within groups with more than 2 individuals, which are best-dealt in the framework of N-Person games. In this Thesis, we investigate the evolutionary dynamics of two paradigmatic collective social dilemmas - the N-Person Prisoner's Dilemma (NPD) and the N-Person Snowdrift Game (NSG) on structured populations, modeled by networks with diverse topological properties. Cooperative strategies are just one example of the many traits that can be transmitted on social networks. Several recent studies based on empirical evidence from a medical database have suggested the existence of a 3 degrees of influence rule, according to which not only our "friends", but also our friends' friends, and our friends' friends' friends, have a non-trivial influence on our decisions. We investigate the degree of peer influence that emerges from the spread of cooperative strategies, opinions and diseases on populations with distinct underlying networks of contacts. Our results show that networks naturally entangle individuals into interactions of many-body nature and that for each network class considered different processes lead to identical degrees of influence. None

Heterogeneous update mechanisms in evolutionary games: Mixing innovative and imitative dynamics.

PubMed

Amaral, Marco Antonio; Javarone, Marco Alberto

2018-04-01

Innovation and evolution are two processes of paramount relevance for social and biological systems. In general, the former allows the introduction of elements of novelty, while the latter is responsible for the motion of a system in its phase space. Often, these processes are strongly related, since an innovation can trigger the evolution, and the latter can provide the optimal conditions for the emergence of innovations. Both processes can be studied by using the framework of evolutionary game theory, where evolution constitutes an intrinsic mechanism. At the same time, the concept of innovation requires an opportune mathematical representation. Notably, innovation can be modeled as a strategy, or it can constitute the underlying mechanism that allows agents to change strategy. Here, we analyze the second case, investigating the behavior of a heterogeneous population, composed of imitative and innovative agents. Imitative agents change strategy only by imitating that of their neighbors, whereas innovative ones change strategy without the need for a copying source. The proposed model is analyzed by means of analytical calculations and numerical simulations in different topologies. Remarkably, results indicate that the mixing of mechanisms can be detrimental to cooperation near phase transitions. In those regions, the spatial reciprocity from imitative mechanisms is destroyed by innovative agents, leading to the downfall of cooperation. Our investigation sheds some light on the complex dynamics emerging from the heterogeneity of strategy revision methods, highlighting the role of innovation in evolutionary games.

Asymmetric Evolutionary Games.

PubMed

McAvoy, Alex; Hauert, Christoph

2015-08-01

Evolutionary game theory is a powerful framework for studying evolution in populations of interacting individuals. A common assumption in evolutionary game theory is that interactions are symmetric, which means that the players are distinguished by only their strategies. In nature, however, the microscopic interactions between players are nearly always asymmetric due to environmental effects, differing baseline characteristics, and other possible sources of heterogeneity. To model these phenomena, we introduce into evolutionary game theory two broad classes of asymmetric interactions: ecological and genotypic. Ecological asymmetry results from variation in the environments of the players, while genotypic asymmetry is a consequence of the players having differing baseline genotypes. We develop a theory of these forms of asymmetry for games in structured populations and use the classical social dilemmas, the Prisoner's Dilemma and the Snowdrift Game, for illustrations. Interestingly, asymmetric games reveal essential differences between models of genetic evolution based on reproduction and models of cultural evolution based on imitation that are not apparent in symmetric games.

A consensus opinion model based on the evolutionary game

NASA Astrophysics Data System (ADS)

Yang, Han-Xin

2016-08-01

We propose a consensus opinion model based on the evolutionary game. In our model, both of the two connected agents receive a benefit if they have the same opinion, otherwise they both pay a cost. Agents update their opinions by comparing payoffs with neighbors. The opinion of an agent with higher payoff is more likely to be imitated. We apply this model in scale-free networks with tunable degree distribution. Interestingly, we find that there exists an optimal ratio of cost to benefit, leading to the shortest consensus time. Qualitative analysis is obtained by examining the evolution of the opinion clusters. Moreover, we find that the consensus time decreases as the average degree of the network increases, but increases with the noise introduced to permit irrational choices. The dependence of the consensus time on the network size is found to be a power-law form. For small or larger ratio of cost to benefit, the consensus time decreases as the degree exponent increases. However, for moderate ratio of cost to benefit, the consensus time increases with the degree exponent. Our results may provide new insights into opinion dynamics driven by the evolutionary game theory.

The Evolution of Cooperation in the Finitely Repeated Prisoner’s Dilemma

DTIC Science & Technology

1989-09-01

biological evolutionary game theory, mathematical ecology (the replicator dynamics are formally equivalent to the Lotka - Volterra dynamics), and...repeated prisoner’s dilemma. Under the dynamics considered, if there is convergence to a limit (in general there need not be), then that limit must...of time. It will be noted also that this same behavior can create computation problems making it imprudent in general to try to infer limiting

Structural symmetry in evolutionary games.

PubMed

McAvoy, Alex; Hauert, Christoph

2015-10-06

In evolutionary game theory, an important measure of a mutant trait (strategy) is its ability to invade and take over an otherwise-monomorphic population. Typically, one quantifies the success of a mutant strategy via the probability that a randomly occurring mutant will fixate in the population. However, in a structured population, this fixation probability may depend on where the mutant arises. Moreover, the fixation probability is just one quantity by which one can measure the success of a mutant; fixation time, for instance, is another. We define a notion of homogeneity for evolutionary games that captures what it means for two single-mutant states, i.e. two configurations of a single mutant in an otherwise-monomorphic population, to be 'evolutionarily equivalent' in the sense that all measures of evolutionary success are the same for both configurations. Using asymmetric games, we argue that the term 'homogeneous' should apply to the evolutionary process as a whole rather than to just the population structure. For evolutionary matrix games in graph-structured populations, we give precise conditions under which the resulting process is homogeneous. Finally, we show that asymmetric matrix games can be reduced to symmetric games if the population structure possesses a sufficient degree of symmetry. © 2015 The Author(s).

Structural symmetry in evolutionary games

PubMed Central

McAvoy, Alex; Hauert, Christoph

2015-01-01

In evolutionary game theory, an important measure of a mutant trait (strategy) is its ability to invade and take over an otherwise-monomorphic population. Typically, one quantifies the success of a mutant strategy via the probability that a randomly occurring mutant will fixate in the population. However, in a structured population, this fixation probability may depend on where the mutant arises. Moreover, the fixation probability is just one quantity by which one can measure the success of a mutant; fixation time, for instance, is another. We define a notion of homogeneity for evolutionary games that captures what it means for two single-mutant states, i.e. two configurations of a single mutant in an otherwise-monomorphic population, to be ‘evolutionarily equivalent’ in the sense that all measures of evolutionary success are the same for both configurations. Using asymmetric games, we argue that the term ‘homogeneous’ should apply to the evolutionary process as a whole rather than to just the population structure. For evolutionary matrix games in graph-structured populations, we give precise conditions under which the resulting process is homogeneous. Finally, we show that asymmetric matrix games can be reduced to symmetric games if the population structure possesses a sufficient degree of symmetry. PMID:26423436

Promotion of cooperation induced by a self-questioning update rule in the spatial traveler's dilemma game

NASA Astrophysics Data System (ADS)

Miao, Qing; Wang, Juan; Hu, Meng-long; Zhang, Fan; Zhang, Qiu-shi; Xia, Cheng-yi

2014-01-01

In sociology and economics, evolutionary game theory has provided a powerful framework to illustrate the social dilemma's problems, and many evolutionary game models are presented, such as prisoner's dilemma game, snowdrift game, public goods game, and so on. In this paper, however, we focus on another typical pair-wise game model: Traveler's Dilemma Game (TDG), which has been deeply investigated in economics, but less attention has been paid to this topic within the physics community. We mainly discuss the influence of strategy update rules on the evolution of cooperation in the spatial TDG, and in detail explore the role of a novel self-questioning or self-learning update mechanism in the evolution of cooperation of the TDG model on the square lattice. In our self-questioning rule, each player does not imitate the strategy state of his or her nearest neighbors and simply plays the traveler's dilemma games twice with nearest neighbors: one is to calculate the actual payoff in the current game round; the other is to perform a virtual game which is used to obtain an intangible payoff if he or she adopts another random strategy. Then, the focal player decides to keep the current strategy or to change into that virtual strategy according to the Fermi-like dynamics. A great number of Monte Carlo simulations indicate that our self-questioning rule is a low information game decision-making mechanism which can greatly promote the evolution of cooperation for some specific conditions in the spatial TDG model. Furthermore, this novel rule can also be applied into the prisoner's dilemma game, and likewise the behavior of cooperation can be largely enhanced. Our results are of high importance to analyze and understand the emergence of cooperation within many real social and economical systems.

Bacteria and game theory: the rise and fall of cooperation in spatially heterogeneous environments.

PubMed

Lambert, Guillaume; Vyawahare, Saurabh; Austin, Robert H

2014-08-06

One of the predictions of game theory is that cooperative behaviours are vulnerable to exploitation by selfish individuals, but this result seemingly contradicts the survival of cooperation observed in nature. In this review, we will introduce game theoretical concepts that lead to this conclusion and show how the spatial competition dynamics between microorganisms can be used to model the survival and maintenance of cooperation. In particular, we focus on how Escherichia coli bacteria with a growth advantage in stationary phase (GASP) phenotype maintain a proliferative phenotype when faced with overcrowding to gain a fitness advantage over wild-type populations. We review recent experimental approaches studying the growth dynamics of competing GASP and wild-type strains of E. coli inside interconnected microfabricated habitats and use a game theoretical approach to analyse the observed inter-species interactions. We describe how the use of evolutionary game theory and the ideal free distribution accurately models the spatial distribution of cooperative and selfish individuals in spatially heterogeneous environments. Using bacteria as a model system of cooperative and selfish behaviours may lead to a better understanding of the competition dynamics of other organisms-including tumour-host interactions during cancer development and metastasis.

Aspiration dynamics and the sustainability of resources in the public goods dilemma

NASA Astrophysics Data System (ADS)

Du, Jinming; Wu, Bin; Wang, Long

2016-04-01

How to exploit public non-renewable resources is a public goods dilemma. Individuals can choose to limit the depletion in order to use the resource for a longer time or consume more goods to benefit themselves. When the resource is used up, there is no benefit for the future generations any more, thus the evolutionary process ends. Here we investigate what mechanisms can extend the use of resources in the framework of evolutionary game theory under two updating rules based on imitation and aspiration, respectively. Compared with imitation process, aspiration dynamics may prolong the sustainable time of a public resource.

A SYMMETRY OF FIXATION TIMES IN EVOULTIONARY DYNAMICS

PubMed Central

TAYLOR, CHRISTINE; IWASA, YOH; NOWAK, MARTIN A.

2010-01-01

In this paper, we show that for evolutionary dynamics between two types that can be described by a Moran process, the conditional fixation time of either type is the same irrespective of the selective scenario. With frequency dependent selection between two strategies A and B of an evolutionary game, regardless of whether A dominates B, A and B are best replies to themselves, or A and B are best replies to each other, the conditional fixation times of a single A and a single B mutant are identical. This does not hold for Wright-Fisher models, nor when the mutants start from multiple copies. PMID:16890959

A study of the dynamics of multi-player games on small networks using territorial interactions.

PubMed

Broom, Mark; Lafaye, Charlotte; Pattni, Karan; Rychtář, Jan

2015-12-01

Recently, the study of structured populations using models of evolutionary processes on graphs has begun to incorporate a more general type of interaction between individuals, allowing multi-player games to be played among the population. In this paper, we develop a birth-death dynamics for use in such models and consider the evolution of populations for special cases of very small graphs where we can easily identify all of the population states and carry out exact analyses. To do so, we study two multi-player games, a Hawk-Dove game and a public goods game. Our focus is on finding the fixation probability of an individual from one type, cooperator or defector in the case of the public goods game, within a population of the other type. We compare this value for both games on several graphs under different parameter values and assumptions, and identify some interesting general features of our model. In particular there is a very close relationship between the fixation probability and the mean temperature, with high temperatures helping fitter individuals and punishing unfit ones and so enhancing selection, whereas low temperatures give a levelling effect which suppresses selection.

Large fluctuations in anti-coordination games on scale-free graphs

NASA Astrophysics Data System (ADS)

Sabsovich, Daniel; Mobilia, Mauro; Assaf, Michael

2017-05-01

We study the influence of the complex topology of scale-free graphs on the dynamics of anti-coordination games (e.g. snowdrift games). These reference models are characterized by the coexistence (evolutionary stable mixed strategy) of two competing species, say ‘cooperators’ and ‘defectors’, and, in finite systems, by metastability and large-fluctuation-driven fixation. In this work, we use extensive computer simulations and an effective diffusion approximation (in the weak selection limit) to determine under which circumstances, depending on the individual-based update rules, the topology drastically affects the long-time behavior of anti-coordination games. In particular, we compute the variance of the number of cooperators in the metastable state and the mean fixation time when the dynamics is implemented according to the voter model (death-first/birth-second process) and the link dynamics (birth/death or death/birth at random). For the voter update rule, we show that the scale-free topology effectively renormalizes the population size and as a result the statistics of observables depend on the network’s degree distribution. In contrast, such a renormalization does not occur with the link dynamics update rule and we recover the same behavior as on complete graphs.

Prediction of stock markets by the evolutionary mix-game model

NASA Astrophysics Data System (ADS)

Chen, Fang; Gou, Chengling; Guo, Xiaoqian; Gao, Jieping

2008-06-01

This paper presents the efforts of using the evolutionary mix-game model, which is a modified form of the agent-based mix-game model, to predict financial time series. Here, we have carried out three methods to improve the original mix-game model by adding the abilities of strategy evolution to agents, and then applying the new model referred to as the evolutionary mix-game model to forecast the Shanghai Stock Exchange Composite Index. The results show that these modifications can improve the accuracy of prediction greatly when proper parameters are chosen.

Asymmetric Evolutionary Games

PubMed Central

McAvoy, Alex; Hauert, Christoph

2015-01-01

Evolutionary game theory is a powerful framework for studying evolution in populations of interacting individuals. A common assumption in evolutionary game theory is that interactions are symmetric, which means that the players are distinguished by only their strategies. In nature, however, the microscopic interactions between players are nearly always asymmetric due to environmental effects, differing baseline characteristics, and other possible sources of heterogeneity. To model these phenomena, we introduce into evolutionary game theory two broad classes of asymmetric interactions: ecological and genotypic. Ecological asymmetry results from variation in the environments of the players, while genotypic asymmetry is a consequence of the players having differing baseline genotypes. We develop a theory of these forms of asymmetry for games in structured populations and use the classical social dilemmas, the Prisoner’s Dilemma and the Snowdrift Game, for illustrations. Interestingly, asymmetric games reveal essential differences between models of genetic evolution based on reproduction and models of cultural evolution based on imitation that are not apparent in symmetric games. PMID:26308326

Game theory in the death galaxy: interaction of cancer and stromal cells in tumour microenvironment.

PubMed

Wu, Amy; Liao, David; Tlsty, Thea D; Sturm, James C; Austin, Robert H

2014-08-06

Preventing relapse is the major challenge to effective therapy in cancer. Within the tumour, stromal (ST) cells play an important role in cancer progression and the emergence of drug resistance. During cancer treatment, the fitness of cancer cells can be enhanced by ST cells because their molecular signalling interaction delays the drug-induced apoptosis of cancer cells. On the other hand, competition among cancer and ST cells for space or resources should not be ignored. We explore the population dynamics of multiple myeloma (MM) versus bone marrow ST cells by using an experimental microecology that we call the death galaxy, with a stable drug gradient and connected microhabitats. Evolutionary game theory is a quantitative way to capture the frequency-dependent nature of interactive populations. Therefore, we use evolutionary game theory to model the populations in the death galaxy with the gradients of pay-offs and successfully predict the future densities of MM and ST cells. We discuss the possible clinical use of such analysis for predicting cancer progression.

Towards a Population Dynamics Theory for Evolutionary Computing: Learning from Biological Population Dynamics in Nature

NASA Astrophysics Data System (ADS)

Ma, Zhanshan (Sam)

In evolutionary computing (EC), population size is one of the critical parameters that a researcher has to deal with. Hence, it was no surprise that the pioneers of EC, such as De Jong (1975) and Holland (1975), had already studied the population sizing from the very beginning of EC. What is perhaps surprising is that more than three decades later, we still largely depend on the experience or ad-hoc trial-and-error approach to set the population size. For example, in a recent monograph, Eiben and Smith (2003) indicated: "In almost all EC applications, the population size is constant and does not change during the evolutionary search." Despite enormous research on this issue in recent years, we still lack a well accepted theory for population sizing. In this paper, I propose to develop a population dynamics theory forEC with the inspiration from the population dynamics theory of biological populations in nature. Essentially, the EC population is considered as a dynamic system over time (generations) and space (search space or fitness landscape), similar to the spatial and temporal dynamics of biological populations in nature. With this conceptual mapping, I propose to 'transplant' the biological population dynamics theory to EC via three steps: (i) experimentally test the feasibility—whether or not emulating natural population dynamics improves the EC performance; (ii) comparatively study the underlying mechanisms—why there are improvements, primarily via statistical modeling analysis; (iii) conduct theoretical analysis with theoretical models such as percolation theory and extended evolutionary game theory that are generally applicable to both EC and natural populations. This article is a summary of a series of studies we have performed to achieve the general goal [27][30]-[32]. In the following, I start with an extremely brief introduction on the theory and models of natural population dynamics (Sections 1 & 2). In Sections 4 to 6, I briefly discuss three categories of population dynamics models: deterministic modeling with Logistic chaos map as an example, stochastic modeling with spatial distribution patterns as an example, as well as survival analysis and extended evolutionary game theory (EEGT) modeling. Sample experiment results with Genetic algorithms (GA) are presented to demonstrate the applications of these models. The proposed EC population dynamics approach also makes survival selection largely unnecessary or much simplified since the individuals are naturally selected (controlled) by the mathematical models for EC population dynamics.

Spatial vs. non-spatial eco-evolutionary dynamics in a tumor growth model.

PubMed

You, Li; Brown, Joel S; Thuijsman, Frank; Cunningham, Jessica J; Gatenby, Robert A; Zhang, Jingsong; Staňková, Kateřina

2017-12-21

Metastatic prostate cancer is initially treated with androgen deprivation therapy (ADT). However, resistance typically develops in about 1 year - a clinical condition termed metastatic castrate-resistant prostate cancer (mCRPC). We develop and investigate a spatial game (agent based continuous space) of mCRPC that considers three distinct cancer cell types: (1) those dependent on exogenous testosterone (T + ), (2) those with increased CYP17A expression that produce testosterone and provide it to the environment as a public good (T P ), and (3) those independent of testosterone (T - ). The interactions within and between cancer cell types can be represented by a 3 × 3 matrix. Based on the known biology of this cancer there are 22 potential matrices that give roughly three major outcomes depending upon the absence (good prognosis), near absence or high frequency (poor prognosis) of T -  cells at the evolutionarily stable strategy (ESS). When just two cell types coexist the spatial game faithfully reproduces the ESS of the corresponding matrix game. With three cell types divergences occur, in some cases just two strategies coexist in the spatial game even as a non-spatial matrix game supports all three. Discrepancies between the spatial game and non-spatial ESS happen because different cell types become more or less clumped in the spatial game - leading to non-random assortative interactions between cell types. Three key spatial scales influence the distribution and abundance of cell types in the spatial game: i. Increasing the radius at which cells interact with each other can lead to higher clumping of each type, ii. Increasing the radius at which cells experience limits to population growth can cause densely packed tumor clusters in space, iii. Increasing the dispersal radius of daughter cells promotes increased mixing of cell types. To our knowledge the effects of these spatial scales on eco-evolutionary dynamics have not been explored in cancer models. The fact that cancer interactions are spatially explicit and that our spatial game of mCRPC provides in general different outcomes than the non-spatial game might suggest that non-spatial models are insufficient for capturing key elements of tumorigenesis. Copyright © 2017 Elsevier Ltd. All rights reserved.

Social evolution and genetic interactions in the short and long term.

PubMed

Van Cleve, Jeremy

2015-08-01

The evolution of social traits remains one of the most fascinating and feisty topics in evolutionary biology even after half a century of theoretical research. W.D. Hamilton shaped much of the field initially with his 1964 papers that laid out the foundation for understanding the effect of genetic relatedness on the evolution of social behavior. Early theoretical investigations revealed two critical assumptions required for Hamilton's rule to hold in dynamical models: weak selection and additive genetic interactions. However, only recently have analytical approaches from population genetics and evolutionary game theory developed sufficiently so that social evolution can be studied under the joint action of selection, mutation, and genetic drift. We review how these approaches suggest two timescales for evolution under weak mutation: (i) a short-term timescale where evolution occurs between a finite set of alleles, and (ii) a long-term timescale where a continuum of alleles are possible and populations evolve continuously from one monomorphic trait to another. We show how Hamilton's rule emerges from the short-term analysis under additivity and how non-additive genetic interactions can be accounted for more generally. This short-term approach reproduces, synthesizes, and generalizes many previous results including the one-third law from evolutionary game theory and risk dominance from economic game theory. Using the long-term approach, we illustrate how trait evolution can be described with a diffusion equation that is a stochastic analogue of the canonical equation of adaptive dynamics. Peaks in the stationary distribution of the diffusion capture classic notions of convergence stability from evolutionary game theory and generally depend on the additive genetic interactions inherent in Hamilton's rule. Surprisingly, the peaks of the long-term stationary distribution can predict the effects of simple kinds of non-additive interactions. Additionally, the peaks capture both weak and strong effects of social payoffs in a manner difficult to replicate with the short-term approach. Together, the results from the short and long-term approaches suggest both how Hamilton's insight may be robust in unexpected ways and how current analytical approaches can expand our understanding of social evolution far beyond Hamilton's original work. Copyright © 2015 Elsevier Inc. All rights reserved.

Promotion of cooperation induced by discriminators in the spatial multi-player donor-recipient game

NASA Astrophysics Data System (ADS)

Cui, Guang-Hai; Wang, Zhen; Ren, Jian-Kang; Lu, Kun; Li, Ming-Chu

2016-11-01

Although the two-player donor-recipient game has been used extensively in studying cooperation in social dilemmas, the scenario in which a donor can simultaneously donate resources to multiple recipients is also common in human societies, economic systems, and social networks. This paper formulates a model of the multi-player donor-recipient game considering a multi-recipient scenario. The promotion of cooperation is also studied by introducing a discriminative cooperation strategy into the game, which donates resources to recipients in proportion to their previous donations with a cost for the collection of information. The evolutionary dynamics of individual strategies are explored in homogeneous and heterogeneous scenarios by leveraging spatial evolutionary game theory. The results show that in a homogeneous scenario, defectors can dominate the network at the equilibrium state only when the cost-to-benefit ratio (R) of donated resources is large. In a heterogeneous scenario, three strategies can coexist all the time within the range of R that was studied, and the promotion of cooperation is more effective when the values of R are smaller. Results from a single node evolution and the formation of local patterns of interaction are provided, and it is analytically shown that discriminators can maintain fairness in resource donation and guarantee long-term cooperation when R is not too large.

System dynamics of behaviour-evolutionary mix-game models

NASA Astrophysics Data System (ADS)

Gou, Cheng-Ling; Gao, Jie-Ping; Chen, Fang

2010-11-01

In real financial markets there are two kinds of traders: one is fundamentalist, and the other is a trend-follower. The mix-game model is proposed to mimic such phenomena. In a mix-game model there are two groups of agents: Group 1 plays the majority game and Group 2 plays the minority game. In this paper, we investigate such a case that some traders in real financial markets could change their investment behaviours by assigning the evolutionary abilities to agents: if the winning rates of agents are smaller than a threshold, they will join the other group; and agents will repeat such an evolution at certain time intervals. Through the simulations, we obtain the following findings: (i) the volatilities of systems increase with the increase of the number of agents in Group 1 and the times of behavioural changes of all agents; (ii) the performances of agents in both groups and the stabilities of systems become better if all agents take more time to observe their new investment behaviours; (iii) there are two-phase zones of market and non-market and two-phase zones of evolution and non-evolution; (iv) parameter configurations located within the cross areas between the zones of markets and the zones of evolution are suited for simulating the financial markets.

Evolutionary dynamics of general group interactions in structured populations

NASA Astrophysics Data System (ADS)

Li, Aming; Broom, Mark; Du, Jinming; Wang, Long

2016-02-01

The evolution of populations is influenced by many factors, and the simple classical models have been developed in a number of important ways. Both population structure and multiplayer interactions have been shown to significantly affect the evolution of important properties, such as the level of cooperation or of aggressive behavior. Here we combine these two key factors and develop the evolutionary dynamics of general group interactions in structured populations represented by regular graphs. The traditional linear and threshold public goods games are adopted as models to address the dynamics. We show that for linear group interactions, population structure can favor the evolution of cooperation compared to the well-mixed case, and we see that the more neighbors there are, the harder it is for cooperators to persist in structured populations. We further show that threshold group interactions could lead to the emergence of cooperation even in well-mixed populations. Here population structure sometimes inhibits cooperation for the threshold public goods game, where depending on the benefit to cost ratio, the outcomes are bistability or a monomorphic population of defectors or cooperators. Our results suggest, counterintuitively, that structured populations are not always beneficial for the evolution of cooperation for nonlinear group interactions.

Effects of behavioral response and vaccination policy on epidemic spreading--an approach based on evolutionary-game dynamics.

PubMed

Zhang, Hai-Feng; Wu, Zhi-Xi; Tang, Ming; Lai, Ying-Cheng

2014-07-11

How effective are governmental incentives to achieve widespread vaccination coverage so as to prevent epidemic outbreak? The answer largely depends on the complex interplay among the type of incentive, individual behavioral responses, and the intrinsic epidemic dynamics. By incorporating evolutionary games into epidemic dynamics, we investigate the effects of two types of incentives strategies: partial-subsidy policy in which certain fraction of the cost of vaccination is offset, and free-subsidy policy in which donees are randomly selected and vaccinated at no cost. Through mean-field analysis and computations, we find that, under the partial-subsidy policy, the vaccination coverage depends monotonically on the sensitivity of individuals to payoff difference, but the dependence is non-monotonous for the free-subsidy policy. Due to the role models of the donees for relatively irrational individuals and the unchanged strategies of the donees for rational individuals, the free-subsidy policy can in general lead to higher vaccination coverage. Our findings indicate that any disease-control policy should be exercised with extreme care: its success depends on the complex interplay among the intrinsic mathematical rules of epidemic spreading, governmental policies, and behavioral responses of individuals.

Effects of behavioral response and vaccination policy on epidemic spreading - an approach based on evolutionary-game dynamics

NASA Astrophysics Data System (ADS)

Zhang, Hai-Feng; Wu, Zhi-Xi; Tang, Ming; Lai, Ying-Cheng

2014-07-01

How effective are governmental incentives to achieve widespread vaccination coverage so as to prevent epidemic outbreak? The answer largely depends on the complex interplay among the type of incentive, individual behavioral responses, and the intrinsic epidemic dynamics. By incorporating evolutionary games into epidemic dynamics, we investigate the effects of two types of incentives strategies: partial-subsidy policy in which certain fraction of the cost of vaccination is offset, and free-subsidy policy in which donees are randomly selected and vaccinated at no cost. Through mean-field analysis and computations, we find that, under the partial-subsidy policy, the vaccination coverage depends monotonically on the sensitivity of individuals to payoff difference, but the dependence is non-monotonous for the free-subsidy policy. Due to the role models of the donees for relatively irrational individuals and the unchanged strategies of the donees for rational individuals, the free-subsidy policy can in general lead to higher vaccination coverage. Our findings indicate that any disease-control policy should be exercised with extreme care: its success depends on the complex interplay among the intrinsic mathematical rules of epidemic spreading, governmental policies, and behavioral responses of individuals.

Epigenetic game theory and its application in plants. Comment on: ;Epigenetic game theory: How to compute the epigenetic control of maternal-to-zygotic transition; by Qian Wang et al.

NASA Astrophysics Data System (ADS)

Zhang, Yuan-Ming; Zhang, Yinghao; Guo, Mingyue

2017-03-01

Wang's et al. article [1] is the first to integrate game theory (especially evolutionary game theory) with epigenetic modification of zygotic genomes. They described and assessed a modeling framework based on evolutionary game theory to quantify, how sperms and oocytes interact through epigenetic processes, to determine embryo development. They also studied the internal mechanisms for normal embryo development: 1) evolutionary interactions between DNA methylation of the paternal and maternal genomes, and 2) the application of game theory to formulate and quantify how different genes compete or cooperate to regulate embryogenesis through methylation. Although it is not very comprehensive and profound regarding game theory modeling, this article bridges the gap between evolutionary game theory and the epigenetic control of embryo development by powerful ordinary differential equations (ODEs). The epiGame framework includes four aspects: 1) characterizing how epigenetic game theory works by the strategy matrix, in which the pattern and relative magnitude of the methylation effects on embryogenesis, are described by the cooperation and competition mechanisms, 2) quantifying the game that the direction and degree of P-M interactions over embryo development can be explained by the sign and magnitude of interaction parameters in model (2), 3) modeling epigenetic interactions within the morula, especially for two coupled nonlinear ODEs, with explicit functions in model (4), which provide a good fit to the observed data for the two sexes (adjusted R2 = 0.956), and 4) revealing multifactorial interactions in embryogenesis from the coupled ODEs in model (2) to triplet ODEs in model (6). Clearly, this article extends game theory from evolutionary game theory to epigenetic game theory.

Evolution and stability of altruist strategies in microbial games

NASA Astrophysics Data System (ADS)

Adami, Christoph; Schossau, Jory; Hintze, Arend

2012-01-01

When microbes compete for limited resources, they often engage in chemical warfare using bacterial toxins. This competition can be understood in terms of evolutionary game theory (EGT). We study the predictions of EGT for the bacterial “suicide bomber” game in terms of the phase portraits of population dynamics, for parameter combinations that cover all interesting games for two-players, and seven of the 38 possible phase portraits of the three-player game. We compare these predictions to simulations of these competitions in finite well-mixed populations, but also allowing for probabilistic rather than pure strategies, as well as Darwinian adaptation over tens of thousands of generations. We find that Darwinian evolution of probabilistic strategies stabilizes games of the rock-paper-scissors type that emerge for parameters describing realistic bacterial populations, and point to ways in which the population fixed point can be selected by changing those parameters.

A new concept: Epigenetic game theory. Comment on: ;Epigenetic game theory: How to compute the epigenetic control of maternal-to-zygotic transition; by Qian Wang et al.

NASA Astrophysics Data System (ADS)

Zheng, Xiu-Deng; Tao, Yi

2017-03-01

The evolutionary significance of the interaction between paternal and maternal genomes in fertilized zygotes is a very interesting and challenging question. Wang et al. developed the concept of epigenetic game theory, and they try to use this concept to explain the interaction between paternal and maternal genomes in fertilized zygotes [1]. They emphasize that the embryogenesis can be considered as an ecological system in which two highly distinct and specialized gametes coordinate through either cooperation or competition, or both, to maximize the fitness of embryos under Darwinian selection. More specifically, they integrate game theory to model the pattern of coordination of paternal genome and maternal genomes mediated by DNA methylation dynamics, and they called this epigenetic game theory.

Optimality and stability of symmetric evolutionary games with applications in genetic selection.

PubMed

Huang, Yuanyuan; Hao, Yiping; Wang, Min; Zhou, Wen; Wu, Zhijun

2015-06-01

Symmetric evolutionary games, i.e., evolutionary games with symmetric fitness matrices, have important applications in population genetics, where they can be used to model for example the selection and evolution of the genotypes of a given population. In this paper, we review the theory for obtaining optimal and stable strategies for symmetric evolutionary games, and provide some new proofs and computational methods. In particular, we review the relationship between the symmetric evolutionary game and the generalized knapsack problem, and discuss the first and second order necessary and sufficient conditions that can be derived from this relationship for testing the optimality and stability of the strategies. Some of the conditions are given in different forms from those in previous work and can be verified more efficiently. We also derive more efficient computational methods for the evaluation of the conditions than conventional approaches. We demonstrate how these conditions can be applied to justifying the strategies and their stabilities for a special class of genetic selection games including some in the study of genetic disorders.

Strategic tradeoffs in competitor dynamics on adaptive networks.

PubMed

Hébert-Dufresne, Laurent; Allard, Antoine; Noël, Pierre-André; Young, Jean-Gabriel; Libby, Eric

2017-08-08

Recent empirical work highlights the heterogeneity of social competitions such as political campaigns: proponents of some ideologies seek debate and conversation, others create echo chambers. While symmetric and static network structure is typically used as a substrate to study such competitor dynamics, network structure can instead be interpreted as a signature of the competitor strategies, yielding competition dynamics on adaptive networks. Here we demonstrate that tradeoffs between aggressiveness and defensiveness (i.e., targeting adversaries vs. targeting like-minded individuals) creates paradoxical behaviour such as non-transitive dynamics. And while there is an optimal strategy in a two competitor system, three competitor systems have no such solution; the introduction of extreme strategies can easily affect the outcome of a competition, even if the extreme strategies have no chance of winning. Not only are these results reminiscent of classic paradoxical results from evolutionary game theory, but the structure of social networks created by our model can be mapped to particular forms of payoff matrices. Consequently, social structure can act as a measurable metric for social games which in turn allows us to provide a game theoretical perspective on online political debates.

Symmetric Decomposition of Asymmetric Games.

PubMed

Tuyls, Karl; Pérolat, Julien; Lanctot, Marc; Ostrovski, Georg; Savani, Rahul; Leibo, Joel Z; Ord, Toby; Graepel, Thore; Legg, Shane

2018-01-17

We introduce new theoretical insights into two-population asymmetric games allowing for an elegant symmetric decomposition into two single population symmetric games. Specifically, we show how an asymmetric bimatrix game (A,B) can be decomposed into its symmetric counterparts by envisioning and investigating the payoff tables (A and B) that constitute the asymmetric game, as two independent, single population, symmetric games. We reveal several surprising formal relationships between an asymmetric two-population game and its symmetric single population counterparts, which facilitate a convenient analysis of the original asymmetric game due to the dimensionality reduction of the decomposition. The main finding reveals that if (x,y) is a Nash equilibrium of an asymmetric game (A,B), this implies that y is a Nash equilibrium of the symmetric counterpart game determined by payoff table A, and x is a Nash equilibrium of the symmetric counterpart game determined by payoff table B. Also the reverse holds and combinations of Nash equilibria of the counterpart games form Nash equilibria of the asymmetric game. We illustrate how these formal relationships aid in identifying and analysing the Nash structure of asymmetric games, by examining the evolutionary dynamics of the simpler counterpart games in several canonical examples.

Study on system dynamics of evolutionary mix-game models

NASA Astrophysics Data System (ADS)

Gou, Chengling; Guo, Xiaoqian; Chen, Fang

2008-11-01

Mix-game model is ameliorated from an agent-based MG model, which is used to simulate the real financial market. Different from MG, there are two groups of agents in Mix-game: Group 1 plays a majority game and Group 2 plays a minority game. These two groups of agents have different bounded abilities to deal with historical information and to count their own performance. In this paper, we modify Mix-game model by assigning the evolution abilities to agents: if the winning rates of agents are smaller than a threshold, they will copy the best strategies the other agent has; and agents will repeat such evolution at certain time intervals. Through simulations this paper finds: (1) the average winning rates of agents in Group 1 and the mean volatilities increase with the increases of the thresholds of Group 1; (2) the average winning rates of both groups decrease but the mean volatilities of system increase with the increase of the thresholds of Group 2; (3) the thresholds of Group 2 have greater impact on system dynamics than the thresholds of Group 1; (4) the characteristics of system dynamics under different time intervals of strategy change are similar to each other qualitatively, but they are different quantitatively; (5) As the time interval of strategy change increases from 1 to 20, the system behaves more and more stable and the performances of agents in both groups become better also.

Chimera states in a network-organized public goods game with destructive agents

NASA Astrophysics Data System (ADS)

Kouvaris, Nikos E.; Requejo, Rubén J.; Hizanidis, Johanne; Díaz-Guilera, Albert

2016-12-01

We found that a network-organized metapopulation of cooperators, defectors, and destructive agents playing the public goods game with mutations can collectively reach global synchronization or chimera states. Global synchronization is accompanied by a collective periodic burst of cooperation, whereas chimera states reflect the tendency of the networked metapopulation to be fragmented in clusters of synchronous and incoherent bursts of cooperation. Numerical simulations have shown that the system's dynamics switches between these two steady states through a first order transition. Depending on the parameters determining the dynamical and topological properties, chimera states with different numbers of coherent and incoherent clusters are observed. Our results present the first systematic study of chimera states and their characterization in the context of evolutionary game theory. This provides a valuable insight into the details of their occurrence, extending the relevance of such states to natural and social systems.

A Strategic Interaction Model of Punishment Favoring Contagion of Honest Behavior

PubMed Central

Cremene, Marcel; Dumitrescu, D.; Cremene, Ligia

2014-01-01

The punishment effect on social behavior is analyzed within the strategic interaction framework of Cellular Automata and computational Evolutionary Game Theory. A new game, called Social Honesty (SH), is proposed. The SH game is analyzed in spatial configurations. Probabilistic punishment is used as a dishonesty deterrence mechanism. In order to capture the intrinsic uncertainty of social environments, payoffs are described as random variables. New dynamics, with a new relation between punishment probability and punishment severity, are revealed. Punishment probability proves to be more important than punishment severity in guiding convergence towards honesty as predominant behavior. This result is confirmed by empirical evidence and reported experiments. Critical values and transition intervals for punishment probability and severity are identified and analyzed. Clusters of honest or dishonest players emerge spontaneously from the very first rounds of interaction and are determinant for the future dynamics and outcomes. PMID:24489917

Strong solutions and instability for the fitness gradient system in evolutionary games between two populations

NASA Astrophysics Data System (ADS)

Xu, Qiuju; Belmonte, Andrew; deForest, Russ; Liu, Chun; Tan, Zhong

2017-04-01

In this paper, we study a fitness gradient system for two populations interacting via a symmetric game. The population dynamics are governed by a conservation law, with a spatial migration flux determined by the fitness. By applying the Galerkin method, we establish the existence, regularity and uniqueness of global solutions to an approximate system, which retains most of the interesting mathematical properties of the original fitness gradient system. Furthermore, we show that a Turing instability occurs for equilibrium states of the fitness gradient system, and its approximations.

The ecology of cancer from an evolutionary game theory perspective.

PubMed

Pacheco, Jorge M; Santos, Francisco C; Dingli, David

2014-08-06

The accumulation of somatic mutations, to which the cellular genome is permanently exposed, often leads to cancer. Analysis of any tumour shows that, besides the malignant cells, one finds other 'supporting' cells such as fibroblasts, immune cells of various types and even blood vessels. Together, these cells generate the microenvironment that enables the malignant cell population to grow and ultimately lead to disease. Therefore, understanding the dynamics of tumour growth and response to therapy is incomplete unless the interactions between the malignant cells and normal cells are investigated in the environment in which they take place. The complex interactions between cells in such an ecosystem result from the exchange of information in the form of cytokines- and adhesion-dependent interactions. Such processes impose costs and benefits to the participating cells that may be conveniently recast in the form of a game pay-off matrix. As a result, tumour progression and dynamics can be described in terms of evolutionary game theory (EGT), which provides a convenient framework in which to capture the frequency-dependent nature of ecosystem dynamics. Here, we provide a tutorial review of the central aspects of EGT, establishing a relation with the problem of cancer. Along the way, we also digress on fitness and of ways to compute it. Subsequently, we show how EGT can be applied to the study of the various manifestations and dynamics of multiple myeloma bone disease and its preceding condition known as monoclonal gammopathy of undetermined significance. We translate the complex biochemical signals into costs and benefits of different cell types, thus defining a game pay-off matrix. Then we use the well-known properties of the EGT equations to reduce the number of core parameters that characterize disease evolution. Finally, we provide an interpretation of these core parameters in terms of what their function is in the ecosystem we are describing and generate predictions on the type and timing of interventions that can alter the natural history of these two conditions.

Le Chatelier's principle in replicator dynamics

NASA Astrophysics Data System (ADS)

Allahverdyan, Armen E.; Galstyan, Aram

2011-10-01

The Le Chatelier principle states that physical equilibria are not only stable, but they also resist external perturbations via short-time negative-feedback mechanisms: a perturbation induces processes tending to diminish its results. The principle has deep roots, e.g., in thermodynamics it is closely related to the second law and the positivity of the entropy production. Here we study the applicability of the Le Chatelier principle to evolutionary game theory, i.e., to perturbations of a Nash equilibrium within the replicator dynamics. We show that the principle can be reformulated as a majorization relation. This defines a stability notion that generalizes the concept of evolutionary stability. We determine criteria for a Nash equilibrium to satisfy the Le Chatelier principle and relate them to mutualistic interactions (game-theoretical anticoordination) showing in which sense mutualistic replicators can be more stable than (say) competing ones. There are globally stable Nash equilibria, where the Le Chatelier principle is violated even locally: in contrast to the thermodynamic equilibrium a Nash equilibrium can amplify small perturbations, though both types of equilibria satisfy the detailed balance condition.

Le Chatelier's principle in replicator dynamics.

PubMed

Allahverdyan, Armen E; Galstyan, Aram

2011-10-01

The Le Chatelier principle states that physical equilibria are not only stable, but they also resist external perturbations via short-time negative-feedback mechanisms: a perturbation induces processes tending to diminish its results. The principle has deep roots, e.g., in thermodynamics it is closely related to the second law and the positivity of the entropy production. Here we study the applicability of the Le Chatelier principle to evolutionary game theory, i.e., to perturbations of a Nash equilibrium within the replicator dynamics. We show that the principle can be reformulated as a majorization relation. This defines a stability notion that generalizes the concept of evolutionary stability. We determine criteria for a Nash equilibrium to satisfy the Le Chatelier principle and relate them to mutualistic interactions (game-theoretical anticoordination) showing in which sense mutualistic replicators can be more stable than (say) competing ones. There are globally stable Nash equilibria, where the Le Chatelier principle is violated even locally: in contrast to the thermodynamic equilibrium a Nash equilibrium can amplify small perturbations, though both types of equilibria satisfy the detailed balance condition.

MMP-TIMP interactions in cancer invasion: An evolutionary game-theoretical framework.

PubMed

Salimi Sartakhti, Javad; Manshaei, Mohammad Hossein; Sadeghi, Mehdi

2017-01-07

One of the main steps in solid cancers to invade surrounding tissues is degradation of tissue barriers in the extracellular matrix. This operation that leads to initiate, angiogenesis and metastasis to other organs, is essentially consequence of collapsing dynamic balance between matrix metalloproteinases (MMP) and tissue inhibitors of metalloproteinases (TIMP). In this work, we model the MMP-TIMP interaction in both normal tissue and invasive cancer using evolutionary game theory. Our model explains how invasive cancer cells get the upper hand in MMP-TIMP imbalance scenarios. We investigate dynamics of them over time and discuss stable and nonstable states in the population. Numerical simulations presented here provide the identification of key genotypic features in the tumor invasion and a natural description for phenotypic variability. The simulation results are consistent with the experimental results in vitro observations presented in medical literature. Finally, by the provided results the necessary conditions to inhibit cancer invasion or prolong its course are explained. In this way, two therapeutic approaches with respect to how they could meet the required conditions are considered. Copyright © 2016 Elsevier Ltd. All rights reserved.

Modeling adaptation of wetland plants under changing environments

NASA Astrophysics Data System (ADS)

Muneepeerakul, R.; Muneepeerakul, C. P.

2010-12-01

An evolutionary-game-theoretic approach is used to study the changes in traits of wetland plants in response to environmental changes, e.g., altered patterns of rainfall and nutrients. Here, a wetland is considered as a complex adaptive system where plants can adapt their strategies and influence one another. The system is subject to stochastic rainfall, which controls the dynamics of water level, soil moisture, and alternation between aerobic and anaerobic conditions in soil. Based on our previous work, a plant unit is characterized by three traits, namely biomass nitrogen content, specific leaf area, and allocation to rhizome. These traits control the basic functions of plants such as assimilation, respiration, and nutrient uptake, while affecting their environment through litter chemistry, root oxygenation, and thus soil microbial dynamics. The outcome of this evolutionary game, i.e., the best-performing plant traits against the backdrop of these interactions and feedbacks, is analyzed and its implications on important roles of wetlands in supporting our sustainability such as carbon sequestration in biosphere, nutrient cycling, and repository of biodiversity are discussed.

A strategy with novel evolutionary features for the iterated prisoner's dilemma.

PubMed

Li, Jiawei; Kendall, Graham

2009-01-01

In recent iterated prisoner's dilemma tournaments, the most successful strategies were those that had identification mechanisms. By playing a predetermined sequence of moves and learning from their opponents' responses, these strategies managed to identify their opponents. We believe that these identification mechanisms may be very useful in evolutionary games. In this paper one such strategy, which we call collective strategy, is analyzed. Collective strategies apply a simple but efficient identification mechanism (that just distinguishes themselves from other strategies), and this mechanism allows them to only cooperate with their group members and defect against any others. In this way, collective strategies are able to maintain a stable population in evolutionary iterated prisoner's dilemma. By means of an invasion barrier, this strategy is compared with other strategies in evolutionary dynamics in order to demonstrate its evolutionary features. We also find that this collective behavior assists the evolution of cooperation in specific evolutionary environments.

Game dynamic model for yeast development.

PubMed

Huang, Yuanyuan; Wu, Zhijun

2012-07-01

Game theoretic models, along with replicator equations, have been applied successfully to the study of evolution of populations of competing species, including the growth of a population, the reaching of the population to an equilibrium state, and the evolutionary stability of the state. In this paper, we analyze a game model proposed by Gore et al. (Nature 456:253-256, 2009) in their recent study on the co-development of two mixed yeast strains. We examine the mathematical properties of this model with varying experimental parameters. We simulate the growths of the yeast strains and compare them with the experimental results. We also compute and analyze the equilibrium state of the system and prove that it is asymptotically and evolutionarily stable.

Evolutionary dynamics on any population structure

NASA Astrophysics Data System (ADS)

Allen, Benjamin; Lippner, Gabor; Chen, Yu-Ting; Fotouhi, Babak; Momeni, Naghmeh; Yau, Shing-Tung; Nowak, Martin A.

2017-03-01

Evolution occurs in populations of reproducing individuals. The structure of a population can affect which traits evolve. Understanding evolutionary game dynamics in structured populations remains difficult. Mathematical results are known for special structures in which all individuals have the same number of neighbours. The general case, in which the number of neighbours can vary, has remained open. For arbitrary selection intensity, the problem is in a computational complexity class that suggests there is no efficient algorithm. Whether a simple solution for weak selection exists has remained unanswered. Here we provide a solution for weak selection that applies to any graph or network. Our method relies on calculating the coalescence times of random walks. We evaluate large numbers of diverse population structures for their propensity to favour cooperation. We study how small changes in population structure—graph surgery—affect evolutionary outcomes. We find that cooperation flourishes most in societies that are based on strong pairwise ties.

Cooperation enhanced by the coevolution of teaching activity in evolutionary prisoner's dilemma games with voluntary participation.

PubMed

Shen, Chen; Chu, Chen; Geng, Yini; Jin, Jiahua; Chen, Fei; Shi, Lei

2018-01-01

Voluntary participation, as an additional strategy involved in repeated games, has been proved to be an efficient way to promote the evolution of cooperation theoretically and empirically. Besides, current studies show that the coevolution of teaching activity can promote cooperation. Thus, inspired by aforementioned above, we investigate the effect of coevolution of teaching activity on the evolution of cooperation for prisoner's dilemma game with voluntary participation: when the focal player successfully enforces its strategy on the opponent, his teaching ability will get an increase. Through numerical simulation, we have shown that voluntary participation could effectively promote the fraction of cooperation, which is also affected by the value of increment. Furthermore, we investigate the influence of the increment value on the density of different strategies and find that there exists an optimal increment value that plays an utmost role on the evolutionary dynamics. With regard to this observation, we unveil that an optimal value of increment can lead to strongest heterogeneity in agents' teaching ability, further promoting the evolution of cooperation.

Strict or graduated punishment? Effect of punishment strictness on the evolution of cooperation in continuous public goods games.

PubMed

Shimao, Hajime; Nakamaru, Mayuko

2013-01-01

Whether costly punishment encourages cooperation is one of the principal questions in studies on the evolution of cooperation and social sciences. In society, punishment helps deter people from flouting rules in institutions. Specifically, graduated punishment is a design principle for long-enduring common-pool resource institutions. In this study, we investigate whether graduated punishment can promote a higher cooperation level when each individual plays the public goods game and has the opportunity to punish others whose cooperation levels fall below the punisher's threshold. We then examine how spatial structure affects evolutionary dynamics when each individual dies inversely proportional to the game score resulting from the social interaction and another player is randomly chosen from the population to produce offspring to fill the empty site created after a player's death. Our evolutionary simulation outcomes demonstrate that stricter punishment promotes increased cooperation more than graduated punishment in a spatially structured population, whereas graduated punishment increases cooperation more than strict punishment when players interact with randomly chosen opponents from the population. The mathematical analysis also supports the results.

Strict or Graduated Punishment? Effect of Punishment Strictness on the Evolution of Cooperation in Continuous Public Goods Games

PubMed Central

Shimao, Hajime; Nakamaru, Mayuko

2013-01-01

Whether costly punishment encourages cooperation is one of the principal questions in studies on the evolution of cooperation and social sciences. In society, punishment helps deter people from flouting rules in institutions. Specifically, graduated punishment is a design principle for long-enduring common-pool resource institutions. In this study, we investigate whether graduated punishment can promote a higher cooperation level when each individual plays the public goods game and has the opportunity to punish others whose cooperation levels fall below the punisher’s threshold. We then examine how spatial structure affects evolutionary dynamics when each individual dies inversely proportional to the game score resulting from the social interaction and another player is randomly chosen from the population to produce offspring to fill the empty site created after a player’s death. Our evolutionary simulation outcomes demonstrate that stricter punishment promotes increased cooperation more than graduated punishment in a spatially structured population, whereas graduated punishment increases cooperation more than strict punishment when players interact with randomly chosen opponents from the population. The mathematical analysis also supports the results. PMID:23555826

Evolutionary stability in continuous nonlinear public goods games.

PubMed

Molina, Chai; Earn, David J D

2017-01-01

We investigate a type of public goods games played in groups of individuals who choose how much to contribute towards the production of a common good, at a cost to themselves. In these games, the common good is produced based on the sum of contributions from all group members, then equally distributed among them. In applications, the dependence of the common good on the total contribution is often nonlinear (e.g., exhibiting synergy or diminishing returns). To date, most theoretical and experimental studies have addressed scenarios in which the set of possible contributions is discrete. However, in many real-world situations, contributions are continuous (e.g., individuals volunteering their time). The "n-player snowdrift games" that we analyze involve continuously varying contributions. We establish under what conditions populations of contributing (or "cooperating") individuals can evolve and persist. Previous work on snowdrift games, using adaptive dynamics, has found that what we term an "equally cooperative" strategy is locally convergently and evolutionarily stable. Using static evolutionary game theory, we find conditions under which this strategy is actually globally evolutionarily stable. All these results refer to stability to invasion by a single mutant. We broaden the scope of existing stability results by showing that the equally cooperative strategy is locally stable to potentially large population perturbations, i.e., allowing for the possibility that mutants make up a non-negligible proportion of the population (due, for example, to genetic drift, environmental variability or dispersal).

Diverse strategy-learning styles promote cooperation in evolutionary spatial prisoner's dilemma game

NASA Astrophysics Data System (ADS)

Liu, Run-Ran; Jia, Chun-Xiao; Rong, Zhihai

2015-11-01

Observational learning and practice learning are two important learning styles and play important roles in our information acquisition. In this paper, we study a spacial evolutionary prisoner's dilemma game, where players can choose the observational learning rule or the practice learning rule when updating their strategies. In the proposed model, we use a parameter p controlling the preference of players choosing the observational learning rule, and found that there exists an optimal value of p leading to the highest cooperation level, which indicates that the cooperation can be promoted by these two learning rules collaboratively and one single learning rule is not favor the promotion of cooperation. By analysing the dynamical behavior of the system, we find that the observational learning rule can make the players residing on cooperative clusters more easily realize the bad sequence of mutual defection. However, a too high observational learning probability suppresses the players to form compact cooperative clusters. Our results highlight the importance of a strategy-updating rule, more importantly, the observational learning rule in the evolutionary cooperation.

Fixation of strategies driven by switching probabilities in evolutionary games

NASA Astrophysics Data System (ADS)

Xu, Zimin; Zhang, Jianlei; Zhang, Chunyan; Chen, Zengqiang

2016-12-01

We study the evolutionary dynamics of strategies in finite populations which are homogeneous and well mixed by means of the pairwise comparison process, the core of which is the proposed switching probability. Previous studies about this subject are usually based on the known payoff comparison of the related players, which is an ideal assumption. In real social systems, acquiring the accurate payoffs of partners at each round of interaction may be not easy. So we bypass the need of explicit knowledge of payoffs, and encode the payoffs into the willingness of any individual shift from her current strategy to the competing one, and the switching probabilities are wholly independent of payoffs. Along this way, the strategy updating can be performed when game models are fixed and payoffs are unclear, expected to extend ideal assumptions to be more realistic one. We explore the impact of the switching probability on the fixation probability and derive a simple formula which determines the fixation probability. Moreover we find that cooperation dominates defection if the probability of cooperation replacing defection is always larger than the probability of defection replacing cooperation in finite populations. Last, we investigate the influences of model parameters on the fixation of strategies in the framework of three concrete game models: prisoner's dilemma, snowdrift game and stag-hunt game, which effectively portray the characteristics of cooperative dilemmas in real social systems.

The puzzle of partial migration: Adaptive dynamics and evolutionary game theory perspectives.

PubMed

De Leenheer, Patrick; Mohapatra, Anushaya; Ohms, Haley A; Lytle, David A; Cushing, J M

2017-01-07

We consider the phenomenon of partial migration which is exhibited by populations in which some individuals migrate between habitats during their lifetime, but others do not. First, using an adaptive dynamics approach, we show that partial migration can be explained on the basis of negative density dependence in the per capita fertilities alone, provided that this density dependence is attenuated for increasing abundances of the subtypes that make up the population. We present an exact formula for the optimal proportion of migrants which is expressed in terms of the vital rates of migrant and non-migrant subtypes only. We show that this allocation strategy is both an evolutionary stable strategy (ESS) as well as a convergence stable strategy (CSS). To establish the former, we generalize the classical notion of an ESS because it is based on invasion exponents obtained from linearization arguments, which fail to capture the stabilizing effects of the nonlinear density dependence. These results clarify precisely when the notion of a "weak ESS", as proposed in Lundberg (2013) for a related model, is a genuine ESS. Secondly, we use an evolutionary game theory approach, and confirm, once again, that partial migration can be attributed to negative density dependence alone. In this context, the result holds even when density dependence is not attenuated. In this case, the optimal allocation strategy towards migrants is the same as the ESS stemming from the analysis based on the adaptive dynamics. The key feature of the population models considered here is that they are monotone dynamical systems, which enables a rather comprehensive mathematical analysis. Copyright © 2016 Elsevier Ltd. All rights reserved.

Evolutionary Game Theory Analysis of Tumor Progression

NASA Astrophysics Data System (ADS)

Wu, Amy; Liao, David; Sturm, James; Austin, Robert

2014-03-01

Evolutionary game theory applied to two interacting cell populations can yield quantitative prediction of the future densities of the two cell populations based on the initial interaction terms. We will discuss how in a complex ecology that evolutionary game theory successfully predicts the future densities of strains of stromal and cancer cells (multiple myeloma), and discuss the possible clinical use of such analysis for predicting cancer progression. Supported by the National Science Foundation and the National Cancer Institute.

The evolution of cooperation on geographical networks

NASA Astrophysics Data System (ADS)

Li, Yixiao; Wang, Yi; Sheng, Jichuan

2017-11-01

We study evolutionary public goods game on geographical networks, i.e., complex networks which are located on a geographical plane. The geographical feature effects in two ways: In one way, the geographically-induced network structure influences the overall evolutionary dynamics, and, in the other way, the geographical length of an edge influences the cost when the two players at the two ends interact. For the latter effect, we design a new cost function of cooperators, which simply assumes that the longer the distance between two players, the higher cost the cooperator(s) of them have to pay. In this study, network substrates are generated by a previous spatial network model with a cost-benefit parameter controlling the network topology. Our simulations show that the greatest promotion of cooperation is achieved in the intermediate regime of the parameter, in which empirical estimates of various railway networks fall. Further, we investigate how the distribution of edges' geographical costs influences the evolutionary dynamics and consider three patterns of the distribution: an approximately-equal distribution, a diverse distribution, and a polarized distribution. For normal geographical networks which are generated using intermediate values of the cost-benefit parameter, a diverse distribution hinders the evolution of cooperation, whereas a polarized distribution lowers the threshold value of the amplification factor for cooperation in public goods game. These results are helpful for understanding the evolution of cooperation on real-world geographical networks.

An oscillating tragedy of the commons in replicator dynamics with game-environment feedback.

PubMed

Weitz, Joshua S; Eksin, Ceyhun; Paarporn, Keith; Brown, Sam P; Ratcliff, William C

2016-11-22

A tragedy of the commons occurs when individuals take actions to maximize their payoffs even as their combined payoff is less than the global maximum had the players coordinated. The originating example is that of overgrazing of common pasture lands. In game-theoretic treatments of this example, there is rarely consideration of how individual behavior subsequently modifies the commons and associated payoffs. Here, we generalize evolutionary game theory by proposing a class of replicator dynamics with feedback-evolving games in which environment-dependent payoffs and strategies coevolve. We initially apply our formulation to a system in which the payoffs favor unilateral defection and cooperation, given replete and depleted environments, respectively. Using this approach, we identify and characterize a class of dynamics: an oscillatory tragedy of the commons in which the system cycles between deplete and replete environmental states and cooperation and defection behavior states. We generalize the approach to consider outcomes given all possible rational choices of individual behavior in the depleted state when defection is favored in the replete state. In so doing, we find that incentivizing cooperation when others defect in the depleted state is necessary to avert the tragedy of the commons. In closing, we propose directions for the study of control and influence in games in which individual actions exert a substantive effect on the environmental state.

An oscillating tragedy of the commons in replicator dynamics with game-environment feedback

PubMed Central

Weitz, Joshua S.; Eksin, Ceyhun; Paarporn, Keith; Brown, Sam P.; Ratcliff, William C.

2016-01-01

A tragedy of the commons occurs when individuals take actions to maximize their payoffs even as their combined payoff is less than the global maximum had the players coordinated. The originating example is that of overgrazing of common pasture lands. In game-theoretic treatments of this example, there is rarely consideration of how individual behavior subsequently modifies the commons and associated payoffs. Here, we generalize evolutionary game theory by proposing a class of replicator dynamics with feedback-evolving games in which environment-dependent payoffs and strategies coevolve. We initially apply our formulation to a system in which the payoffs favor unilateral defection and cooperation, given replete and depleted environments, respectively. Using this approach, we identify and characterize a class of dynamics: an oscillatory tragedy of the commons in which the system cycles between deplete and replete environmental states and cooperation and defection behavior states. We generalize the approach to consider outcomes given all possible rational choices of individual behavior in the depleted state when defection is favored in the replete state. In so doing, we find that incentivizing cooperation when others defect in the depleted state is necessary to avert the tragedy of the commons. In closing, we propose directions for the study of control and influence in games in which individual actions exert a substantive effect on the environmental state. PMID:27830651

Spatial structure favors cooperative behavior in the snowdrift game with multiple interactive dynamics

NASA Astrophysics Data System (ADS)

Su, Qi; Li, Aming; Wang, Long

2017-02-01

Spatial reciprocity is generally regarded as a positive rule facilitating the evolution of cooperation. However, a few recent studies show that, in the snowdrift game, spatial structure still could be detrimental to cooperation. Here we propose a model of multiple interactive dynamics, where each individual can cooperate and defect simultaneously against different neighbors. We realize individuals' multiple interactions simply by endowing them with strategies relevant to probabilities, and every one decides to cooperate or defect with a probability. With multiple interactive dynamics, the cooperation level in square lattices is higher than that in the well-mixed case for a wide range of cost-to-benefit ratio r, implying that spatial structure favors cooperative behavior in the snowdrift game. Moreover, in square lattices, the most favorable strategy follows a simple relation of r, which confers theoretically the average evolutionary frequency of cooperative behavior. We further extend our study to various homogeneous and heterogeneous networks, which demonstrates the robustness of our results. Here multiple interactive dynamics stabilizes the positive role of spatial structure on the evolution of cooperation and individuals' distinct reactions to different neighbors can be a new line in understanding the emergence of cooperation.

Double-dealing behavior potentially promotes cooperation in evolutionary prisoner's dilemma games

NASA Astrophysics Data System (ADS)

Dai, Qionglin; Li, Haihong; Cheng, Hongyan; Li, Yuting; Yang, Junzhong

2010-11-01

We investigate the effects of double-dealing behavior on cooperation in evolutionary games. Each individual in a population has two attributes: character and action. One's action may be consistent with one's character or not. We provide analytical results by a mean-field description of evolutionary prisoner's dilemma games (PDGs). Moreover, we give numerical results on different networks, ranging from square lattices to scale-free networks (SFNs). Two important conclusions have been drawn from the results on SFNs. Firstly, if only non-influential individuals (those with low degrees) have chances of becoming double-dealers, cooperation is certain to deteriorate. Secondly, when influential individuals (those with high degrees) adopt double-dealing behavior moderately, cooperation would be enhanced, which is in opposition to the traditional belief. These results help us to understand better the social phenomenon of the existence of double-dealers. In addition to the PDG, other types of games including the snowdrift game, the stag-hunt game and the harmony game have also been studied on our model. The results for these three games are also presented, which are consistent with the results for the PDG qualitatively. Furthermore, we consider our model under the co-evolution framework, in which the probability of an individual changing into a double-dealer and the individual strategy both could evolve during the evolutionary process.

A Study of Driver's Route Choice Behavior Based on Evolutionary Game Theory

PubMed Central

Jiang, Xiaowei; Ji, Yanjie; Deng, Wei

2014-01-01

This paper proposes a route choice analytic method that embeds cumulative prospect theory in evolutionary game theory to analyze how the drivers adjust their route choice behaviors under the influence of the traffic information. A simulated network with two alternative routes and one variable message sign is built to illustrate the analytic method. We assume that the drivers in the transportation system are bounded rational, and the traffic information they receive is incomplete. An evolutionary game model is constructed to describe the evolutionary process of the drivers' route choice decision-making behaviors. Here we conclude that the traffic information plays an important role in the route choice behavior. The driver's route decision-making process develops towards different evolutionary stable states in accordance with different transportation situations. The analysis results also demonstrate that employing cumulative prospect theory and evolutionary game theory to study the driver's route choice behavior is effective. This analytic method provides an academic support and suggestion for the traffic guidance system, and may optimize the travel efficiency to a certain extent. PMID:25610455

A study of driver's route choice behavior based on evolutionary game theory.

PubMed

Jiang, Xiaowei; Ji, Yanjie; Du, Muqing; Deng, Wei

2014-01-01

This paper proposes a route choice analytic method that embeds cumulative prospect theory in evolutionary game theory to analyze how the drivers adjust their route choice behaviors under the influence of the traffic information. A simulated network with two alternative routes and one variable message sign is built to illustrate the analytic method. We assume that the drivers in the transportation system are bounded rational, and the traffic information they receive is incomplete. An evolutionary game model is constructed to describe the evolutionary process of the drivers' route choice decision-making behaviors. Here we conclude that the traffic information plays an important role in the route choice behavior. The driver's route decision-making process develops towards different evolutionary stable states in accordance with different transportation situations. The analysis results also demonstrate that employing cumulative prospect theory and evolutionary game theory to study the driver's route choice behavior is effective. This analytic method provides an academic support and suggestion for the traffic guidance system, and may optimize the travel efficiency to a certain extent.

Modelling the host-pathogen interactions of macrophages and Candida albicans using Game Theory and dynamic optimization.

PubMed

Dühring, Sybille; Ewald, Jan; Germerodt, Sebastian; Kaleta, Christoph; Dandekar, Thomas; Schuster, Stefan

2017-07-01

The release of fungal cells following macrophage phagocytosis, called non-lytic expulsion, is reported for several fungal pathogens. On one hand, non-lytic expulsion may benefit the fungus in escaping the microbicidal environment of the phagosome. On the other hand, the macrophage could profit in terms of avoiding its own lysis and being able to undergo proliferation. To analyse the causes of non-lytic expulsion and the relevance of macrophage proliferation in the macrophage- Candida albicans interaction, we employ Evolutionary Game Theory and dynamic optimization in a sequential manner. We establish a game-theoretical model describing the different strategies of the two players after phagocytosis. Depending on the parameter values, we find four different Nash equilibria and determine the influence of the systems state of the host upon the game. As our Nash equilibria are a direct consequence of the model parameterization, we can depict several biological scenarios. A parameter region, where the host response is robust against the fungal infection, is determined. We further apply dynamic optimization to analyse whether macrophage mitosis is relevant in the host-pathogen interaction of macrophages and C. albicans For this, we study the population dynamics of the macrophage- C. albicans interactions and the corresponding optimal controls for the macrophages, indicating the best macrophage strategy of switching from proliferation to attacking fungal cells. © 2017 The Author(s).

Dynamical tuning for MPC using population games: A water supply network application.

PubMed

Barreiro-Gomez, Julian; Ocampo-Martinez, Carlos; Quijano, Nicanor

2017-07-01

Model predictive control (MPC) is a suitable strategy for the control of large-scale systems that have multiple design requirements, e.g., multiple physical and operational constraints. Besides, an MPC controller is able to deal with multiple control objectives considering them within the cost function, which implies to determine a proper prioritization for each of the objectives. Furthermore, when the system has time-varying parameters and/or disturbances, the appropriate prioritization might vary along the time as well. This situation leads to the need of a dynamical tuning methodology. This paper addresses the dynamical tuning issue by using evolutionary game theory. The advantages of the proposed method are highlighted and tested over a large-scale water supply network with periodic time-varying disturbances. Finally, results are analyzed with respect to a multi-objective MPC controller that uses static tuning. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

On evolutionary spatial heterogeneous games

NASA Astrophysics Data System (ADS)

Fort, H.

2008-03-01

How cooperation between self-interested individuals evolve is a crucial problem, both in biology and in social sciences, that is far from being well understood. Evolutionary game theory is a useful approach to this issue. The simplest model to take into account the spatial dimension in evolutionary games is in terms of cellular automata with just a one-parameter payoff matrix. Here, the effects of spatial heterogeneities of the environment and/or asymmetries in the interactions among the individuals are analysed through different extensions of this model. Instead of using the same universal payoff matrix, bimatrix games in which each cell at site ( i, j) has its own different ‘temptation to defect’ parameter T(i,j) are considered. First, the case in which these individual payoffs are constant in time is studied. Second, an evolving evolutionary spatial game such that T=T(i,j;t), i.e. besides depending on the position evolves (by natural selection), is used to explore the combination of spatial heterogeneity and natural selection of payoff matrices.

Evolutionary game theory: cells as players.

PubMed

Hummert, Sabine; Bohl, Katrin; Basanta, David; Deutsch, Andreas; Werner, Sarah; Theissen, Günter; Schroeter, Anja; Schuster, Stefan

2014-12-01

In two papers we review game theory applications in biology below the level of cognitive living beings. It can be seen that evolution and natural selection replace the rationality of the actors appropriately. Even in these micro worlds, competing situations and cooperative relationships can be found and modeled by evolutionary game theory. Also those units of the lowest levels of life show different strategies for different environmental situations or different partners. We give a wide overview of evolutionary game theory applications to microscopic units. In this first review situations on the cellular level are tackled. In particular metabolic problems are discussed, such as ATP-producing pathways, secretion of public goods and cross-feeding. Further topics are cyclic competition among more than two partners, intra- and inter-cellular signalling, the struggle between pathogens and the immune system, and the interactions of cancer cells. Moreover, we introduce the theoretical basics to encourage scientists to investigate problems in cell biology and molecular biology by evolutionary game theory.

Evolutionary dynamics on graphs

NASA Astrophysics Data System (ADS)

Lieberman, Erez; Hauert, Christoph; Nowak, Martin A.

2005-01-01

Evolutionary dynamics have been traditionally studied in the context of homogeneous or spatially extended populations. Here we generalize population structure by arranging individuals on a graph. Each vertex represents an individual. The weighted edges denote reproductive rates which govern how often individuals place offspring into adjacent vertices. The homogeneous population, described by the Moran process, is the special case of a fully connected graph with evenly weighted edges. Spatial structures are described by graphs where vertices are connected with their nearest neighbours. We also explore evolution on random and scale-free networks. We determine the fixation probability of mutants, and characterize those graphs for which fixation behaviour is identical to that of a homogeneous population. Furthermore, some graphs act as suppressors and others as amplifiers of selection. It is even possible to find graphs that guarantee the fixation of any advantageous mutant. We also study frequency-dependent selection and show that the outcome of evolutionary games can depend entirely on the structure of the underlying graph. Evolutionary graph theory has many fascinating applications ranging from ecology to multi-cellular organization and economics.

The study on knowledge transferring incentive for information system requirement development

DOE Office of Scientific and Technical Information (OSTI.GOV)

Li, Yang

2015-03-10

Information system requirement development is a process of users’ knowledge sharing and transferring. However the tacit requirements developing is a main problem during requirement development process, for the reason of difficult to encoding, express, and communicate. Knowledge fusion and corporate effort is needed to finding tacit requirements. Under this background, our paper try to find out the rule of effort dynamic evolutionary of software developer and user by building an evolutionary game model on the condition of incentive system. And in addition this paper provides an in depth discussion at the end of this paper.

Heterogeneity of link weight and the evolution of cooperation

NASA Astrophysics Data System (ADS)

Iwata, Manabu; Akiyama, Eizo

2016-04-01

In this paper, we investigate the effect of heterogeneity of link weight, heterogeneity of the frequency or amount of interactions among individuals, on the evolution of cooperation. Based on an analysis of the evolutionary prisoner's dilemma game on a weighted one-dimensional lattice network with intra-individual heterogeneity, we confirm that moderate level of link-weight heterogeneity can facilitate cooperation. Furthermore, we identify two key mechanisms by which link-weight heterogeneity promotes the evolution of cooperation: mechanisms for spread and maintenance of cooperation. We also derive the corresponding conditions under which the mechanisms can work through evolutionary dynamics.

Universal effect of dynamical reinforcement learning mechanism in spatial evolutionary games

NASA Astrophysics Data System (ADS)

Zhang, Hai-Feng; Wu, Zhi-Xi; Wang, Bing-Hong

2012-06-01

One of the prototypical mechanisms in understanding the ubiquitous cooperation in social dilemma situations is the win-stay, lose-shift rule. In this work, a generalized win-stay, lose-shift learning model—a reinforcement learning model with dynamic aspiration level—is proposed to describe how humans adapt their social behaviors based on their social experiences. In the model, the players incorporate the information of the outcomes in previous rounds with time-dependent aspiration payoffs to regulate the probability of choosing cooperation. By investigating such a reinforcement learning rule in the spatial prisoner's dilemma game and public goods game, a most noteworthy viewpoint is that moderate greediness (i.e. moderate aspiration level) favors best the development and organization of collective cooperation. The generality of this observation is tested against different regulation strengths and different types of network of interaction as well. We also make comparisons with two recently proposed models to highlight the importance of the mechanism of adaptive aspiration level in supporting cooperation in structured populations.

What Information Theory Says About Best Response and About Binding Contracts

NASA Technical Reports Server (NTRS)

Wolpert, David H.

2004-01-01

Product Distribution (PD) theory is the information-theoretic extension of conventional full- rationality game theory to bounded rational games. Here PD theory is used to investigate games in which the players use bounded rational best-response strategies. This investigation illuminates how to determine the optimal organization chart for a corporation, or more generally how to order the sequence of moves of the players / employees so as to optimize an overall objective function. It is then shown that in the continuum-time limit, bounded rational best response games result in a variant of the replicator dynamics of evolutionary game theory. This variant is then investigated for team games, in which the players share the same utility function, by showing that such continuum- limit bounded rational best response is identical to Newton-Raphson iterative optimization of the shared utility function. Next PD theory is used to investigate changing the coordinate system of the game, i.e., changing the mapping from the joint move of the players to the arguments in the utility functions. Such a change couples those arguments, essentially by making each players move be an offered binding contract.

Mesoscopic interactions and species coexistence in evolutionary game dynamics of cyclic competitions.

PubMed

Cheng, Hongyan; Yao, Nan; Huang, Zi-Gang; Park, Junpyo; Do, Younghae; Lai, Ying-Cheng

2014-12-15

Evolutionary dynamical models for cyclic competitions of three species (e.g., rock, paper, and scissors, or RPS) provide a paradigm, at the microscopic level of individual interactions, to address many issues in coexistence and biodiversity. Real ecosystems often involve competitions among more than three species. By extending the RPS game model to five (rock-paper-scissors-lizard-Spock, or RPSLS) mobile species, we uncover a fundamental type of mesoscopic interactions among subgroups of species. In particular, competitions at the microscopic level lead to the emergence of various local groups in different regions of the space, each involving three species. It is the interactions among the groups that fundamentally determine how many species can coexist. In fact, as the mobility is increased from zero, two transitions can occur: one from a five- to a three-species coexistence state and another from the latter to a uniform, single-species state. We develop a mean-field theory to show that, in order to understand the first transition, group interactions at the mesoscopic scale must be taken into account. Our findings suggest, more broadly, the importance of mesoscopic interactions in coexistence of great many species.

Evolutionary game dynamics of controlled and automatic decision-making

NASA Astrophysics Data System (ADS)

Toupo, Danielle F. P.; Strogatz, Steven H.; Cohen, Jonathan D.; Rand, David G.

2015-07-01

We integrate dual-process theories of human cognition with evolutionary game theory to study the evolution of automatic and controlled decision-making processes. We introduce a model in which agents who make decisions using either automatic or controlled processing compete with each other for survival. Agents using automatic processing act quickly and so are more likely to acquire resources, but agents using controlled processing are better planners and so make more effective use of the resources they have. Using the replicator equation, we characterize the conditions under which automatic or controlled agents dominate, when coexistence is possible and when bistability occurs. We then extend the replicator equation to consider feedback between the state of the population and the environment. Under conditions in which having a greater proportion of controlled agents either enriches the environment or enhances the competitive advantage of automatic agents, we find that limit cycles can occur, leading to persistent oscillations in the population dynamics. Critically, however, these limit cycles only emerge when feedback occurs on a sufficiently long time scale. Our results shed light on the connection between evolution and human cognition and suggest necessary conditions for the rise and fall of rationality.

Evolutionary game dynamics of controlled and automatic decision-making.

PubMed

Toupo, Danielle F P; Strogatz, Steven H; Cohen, Jonathan D; Rand, David G

2015-07-01

We integrate dual-process theories of human cognition with evolutionary game theory to study the evolution of automatic and controlled decision-making processes. We introduce a model in which agents who make decisions using either automatic or controlled processing compete with each other for survival. Agents using automatic processing act quickly and so are more likely to acquire resources, but agents using controlled processing are better planners and so make more effective use of the resources they have. Using the replicator equation, we characterize the conditions under which automatic or controlled agents dominate, when coexistence is possible and when bistability occurs. We then extend the replicator equation to consider feedback between the state of the population and the environment. Under conditions in which having a greater proportion of controlled agents either enriches the environment or enhances the competitive advantage of automatic agents, we find that limit cycles can occur, leading to persistent oscillations in the population dynamics. Critically, however, these limit cycles only emerge when feedback occurs on a sufficiently long time scale. Our results shed light on the connection between evolution and human cognition and suggest necessary conditions for the rise and fall of rationality.

Cooperation in group-structured populations with two layers of interactions

PubMed Central

Zhang, Yanling; Fu, Feng; Chen, Xiaojie; Xie, Guangming; Wang, Long

2015-01-01

Recently there has been a growing interest in studying multiplex networks where individuals are structured in multiple network layers. Previous agent-based simulations of games on multiplex networks reveal rich dynamics arising from interdependency of interactions along each network layer, yet there is little known about analytical conditions for cooperation to evolve thereof. Here we aim to tackle this issue by calculating the evolutionary dynamics of cooperation in group-structured populations with two layers of interactions. In our model, an individual is engaged in two layers of group interactions simultaneously and uses unrelated strategies across layers. Evolutionary competition of individuals is determined by the total payoffs accrued from two layers of interactions. We also consider migration which allows individuals to move to a new group within each layer. An approach combining the coalescence theory with the theory of random walks is established to overcome the analytical difficulty upon local migration. We obtain the exact results for all “isotropic” migration patterns, particularly for migration tuned with varying ranges. When the two layers use one game, the optimal migration ranges are proved identical across layers and become smaller as the migration probability grows. PMID:26632251

Evolutionary games with coordination and self-dependent interactions

NASA Astrophysics Data System (ADS)

Király, Balázs; Szabó, György

2017-01-01

Multistrategy evolutionary games are studied on a square lattice when the pair interactions are composed of coordinations between strategy pairs and an additional term with self-dependent payoff. We describe a method for determining the strength of each elementary coordination component in n -strategy potential games. Using analytical and numerical methods, the presence and absence of Ising-type order-disorder phase transitions are studied when a single pair coordination is extended by some types of self-dependent elementary games. We also introduce noise-dependent three-strategy equivalents of the n -strategy elementary coordination games.

Evolutionary games combining two or three pair coordinations on a square lattice

NASA Astrophysics Data System (ADS)

Király, Balázs; Szabó, György

2017-10-01

We study multiagent logit-rule-driven evolutionary games on a square lattice whose pair interactions are composed of a maximal number of nonoverlapping elementary coordination games describing Ising-type interactions between just two of the available strategies. Using Monte Carlo simulations we investigate the macroscopic noise-level-dependent behavior of the two- and three-pair games and the critical properties of the continuous phase transtitions these systems exhibit. The four-strategy game is shown to be equivalent to a system that consists of two independent and identical Ising models.

Evolutionary games combining two or three pair coordinations on a square lattice.

PubMed

Király, Balázs; Szabó, György

2017-10-01

We study multiagent logit-rule-driven evolutionary games on a square lattice whose pair interactions are composed of a maximal number of nonoverlapping elementary coordination games describing Ising-type interactions between just two of the available strategies. Using Monte Carlo simulations we investigate the macroscopic noise-level-dependent behavior of the two- and three-pair games and the critical properties of the continuous phase transtitions these systems exhibit. The four-strategy game is shown to be equivalent to a system that consists of two independent and identical Ising models.

Cooperation guided by the coexistence of imitation dynamics and aspiration dynamics in structured populations

NASA Astrophysics Data System (ADS)

Xu, Kuangyi; Li, Kun; Cong, Rui; Wang, Long

2017-02-01

In the framework of the evolutionary game theory, two fundamentally different mechanisms, the imitation process and the aspiration-driven dynamics, can be adopted by players to update their strategies. In the former case, individuals imitate the strategy of a more successful peer, while in the latter case individuals change their strategies based on a comparison of payoffs they collect in the game to their own aspiration levels. Here we explore how cooperation evolves for the coexistence of these two dynamics. Intriguingly, cooperation reaches its lowest level when a certain moderate fraction of individuals pick aspiration-level-driven rule while the others choose pairwise comparison rule. Furthermore, when individuals can adjust their update rules besides their strategies, either imitation dynamics or aspiration-driven dynamics will finally take over the entire population, and the stationary cooperation level is determined by the outcome of competition between these two dynamics. We find that appropriate synergetic effects and moderate aspiration level boost the fixation probability of aspiration-driven dynamics most effectively. Our work may be helpful in understanding the cooperative behavior induced by the coexistence of imitation dynamics and aspiration dynamics in the society.

Spatial prisoner's dilemma game with volunteering in Newman-Watts small-world networks

NASA Astrophysics Data System (ADS)

Wu, Zhi-Xi; Xu, Xin-Jian; Chen, Yong; Wang, Ying-Hai

2005-03-01

A modified spatial prisoner’s dilemma game with voluntary participation in Newman-Watts small-world networks is studied. Some reasonable ingredients are introduced to the game evolutionary dynamics: each agent in the network is a pure strategist and can only take one of three strategies (cooperator, defector, and loner); its strategical transformation is associated with both the number of strategical states and the magnitude of average profits, which are adopted and acquired by its coplayers in the previous round of play; a stochastic strategy mutation is applied when it gets into the trouble of local commons that the agent and its neighbors are in the same state and get the same average payoffs. In the case of very low temptation to defect, it is found that agents are willing to participate in the game in typical small-world region and intensive collective oscillations arise in more random region.

Doves and hawks in economics revisited: An evolutionary quantum game theory based analysis of financial crises

NASA Astrophysics Data System (ADS)

Hanauske, Matthias; Kunz, Jennifer; Bernius, Steffen; König, Wolfgang

2010-11-01

The last financial and economic crisis demonstrated the dysfunctional long-term effects of aggressive behaviour in financial markets. Yet, evolutionary game theory predicts that under the condition of strategic dependence a certain degree of aggressive behaviour remains within a given population of agents. However, as a consequence of the financial crisis, it would be desirable to change the “rules of the game” in a way that prevents the occurrence of any aggressive behaviour and thereby also the danger of market crashes. The paper picks up this aspect. Through the extension of the well-known hawk-dove game by a quantum approach, we can show that dependent on entanglement, evolutionary stable strategies also can emerge, which are not predicted by the classical evolutionary game theory and where the total economic population uses a non-aggressive quantum strategy.

Local Nash equilibrium in social networks.

PubMed

Zhang, Yichao; Aziz-Alaoui, M A; Bertelle, Cyrille; Guan, Jihong

2014-08-29

Nash equilibrium is widely present in various social disputes. As of now, in structured static populations, such as social networks, regular, and random graphs, the discussions on Nash equilibrium are quite limited. In a relatively stable static gaming network, a rational individual has to comprehensively consider all his/her opponents' strategies before they adopt a unified strategy. In this scenario, a new strategy equilibrium emerges in the system. We define this equilibrium as a local Nash equilibrium. In this paper, we present an explicit definition of the local Nash equilibrium for the two-strategy games in structured populations. Based on the definition, we investigate the condition that a system reaches the evolutionary stable state when the individuals play the Prisoner's dilemma and snow-drift game. The local Nash equilibrium provides a way to judge whether a gaming structured population reaches the evolutionary stable state on one hand. On the other hand, it can be used to predict whether cooperators can survive in a system long before the system reaches its evolutionary stable state for the Prisoner's dilemma game. Our work therefore provides a theoretical framework for understanding the evolutionary stable state in the gaming populations with static structures.

Local Nash Equilibrium in Social Networks

PubMed Central

Zhang, Yichao; Aziz-Alaoui, M. A.; Bertelle, Cyrille; Guan, Jihong

2014-01-01

Nash equilibrium is widely present in various social disputes. As of now, in structured static populations, such as social networks, regular, and random graphs, the discussions on Nash equilibrium are quite limited. In a relatively stable static gaming network, a rational individual has to comprehensively consider all his/her opponents' strategies before they adopt a unified strategy. In this scenario, a new strategy equilibrium emerges in the system. We define this equilibrium as a local Nash equilibrium. In this paper, we present an explicit definition of the local Nash equilibrium for the two-strategy games in structured populations. Based on the definition, we investigate the condition that a system reaches the evolutionary stable state when the individuals play the Prisoner's dilemma and snow-drift game. The local Nash equilibrium provides a way to judge whether a gaming structured population reaches the evolutionary stable state on one hand. On the other hand, it can be used to predict whether cooperators can survive in a system long before the system reaches its evolutionary stable state for the Prisoner's dilemma game. Our work therefore provides a theoretical framework for understanding the evolutionary stable state in the gaming populations with static structures. PMID:25169150

Local Nash Equilibrium in Social Networks

NASA Astrophysics Data System (ADS)

Zhang, Yichao; Aziz-Alaoui, M. A.; Bertelle, Cyrille; Guan, Jihong

2014-08-01

Nash equilibrium is widely present in various social disputes. As of now, in structured static populations, such as social networks, regular, and random graphs, the discussions on Nash equilibrium are quite limited. In a relatively stable static gaming network, a rational individual has to comprehensively consider all his/her opponents' strategies before they adopt a unified strategy. In this scenario, a new strategy equilibrium emerges in the system. We define this equilibrium as a local Nash equilibrium. In this paper, we present an explicit definition of the local Nash equilibrium for the two-strategy games in structured populations. Based on the definition, we investigate the condition that a system reaches the evolutionary stable state when the individuals play the Prisoner's dilemma and snow-drift game. The local Nash equilibrium provides a way to judge whether a gaming structured population reaches the evolutionary stable state on one hand. On the other hand, it can be used to predict whether cooperators can survive in a system long before the system reaches its evolutionary stable state for the Prisoner's dilemma game. Our work therefore provides a theoretical framework for understanding the evolutionary stable state in the gaming populations with static structures.

Evolution of optimal Hill coefficients in nonlinear public goods games.

PubMed

Archetti, Marco; Scheuring, István

2016-10-07

In evolutionary game theory, the effect of public goods like diffusible molecules has been modelled using linear, concave, sigmoid and step functions. The observation that biological systems are often sigmoid input-output functions, as described by the Hill equation, suggests that a sigmoid function is more realistic. The Michaelis-Menten model of enzyme kinetics, however, predicts a concave function, and while mechanistic explanations of sigmoid kinetics exist, we lack an adaptive explanation: what is the evolutionary advantage of a sigmoid benefit function? We analyse public goods games in which the shape of the benefit function can evolve, in order to determine the optimal and evolutionarily stable Hill coefficients. We find that, while the dynamics depends on whether output is controlled at the level of the individual or the population, intermediate or high Hill coefficients often evolve, leading to sigmoid input-output functions that for some parameters are so steep to resemble a step function (an on-off switch). Our results suggest that, even when the shape of the benefit function is unknown, biological public goods should be modelled using a sigmoid or step function rather than a linear or concave function. Copyright © 2016 Elsevier Ltd. All rights reserved.

Evolutionary dynamics of division of labor games with selfish agents

NASA Astrophysics Data System (ADS)

Zhang, Jianlei; Li, Qiaoyu; Zhang, Chunyan

2017-11-01

The division of labor is one of the most basic and widely studied aspects of collective behavior in natural systems. Studies of division of labor are concerned with the integration of the individual worker behavior into a colony level task organization and with the question of how the regulation of the division of labor may contribute to the colony efficiency. This paper investigates the evolution of the division of labor with three strategies by employing the evolutionary game theory. Thus, these available strategies are, respectively, strategy A (performing task A), strategy B (performing task B), and strategy D (not performing any task but only free riding others' contributions). And, two typical networks (i.e., BA scale-free network and lattice network) are employed here for describing the interaction structure among agents. The theoretical analysis together with simulation results reveal that the division of labor can evolve and leads to players that differ in their tendency to take on a given task. The conditions under which the division of labor evolves depend on the costs for performing the task, the benefits led by performing the task, and the interaction structures among the players who are involved with division of labor games.

Emergence of unusual coexistence states in cyclic game systems.

PubMed

Park, Junpyo; Do, Younghae; Jang, Bongsoo; Lai, Ying-Cheng

2017-08-07

Evolutionary games of cyclic competitions have been extensively studied to gain insights into one of the most fundamental phenomena in nature: biodiversity that seems to be excluded by the principle of natural selection. The Rock-Paper-Scissors (RPS) game of three species and its extensions [e.g., the Rock-Paper-Scissors-Lizard-Spock (RPSLS) game] are paradigmatic models in this field. In all previous studies, the intrinsic symmetry associated with cyclic competitions imposes a limitation on the resulting coexistence states, leading to only selective types of such states. We investigate the effect of nonuniform intraspecific competitions on coexistence and find that a wider spectrum of coexistence states can emerge and persist. This surprising finding is substantiated using three classes of cyclic game models through stability analysis, Monte Carlo simulations and continuous spatiotemporal dynamical evolution from partial differential equations. Our finding indicates that intraspecific competitions or alternative symmetry-breaking mechanisms can promote biodiversity to a broader extent than previously thought.

Evolution of flexibility and rigidity in retaliatory punishment.

PubMed

Morris, Adam; MacGlashan, James; Littman, Michael L; Cushman, Fiery

2017-09-26

Natural selection designs some social behaviors to depend on flexible learning processes, whereas others are relatively rigid or reflexive. What determines the balance between these two approaches? We offer a detailed case study in the context of a two-player game with antisocial behavior and retaliatory punishment. We show that each player in this game-a "thief" and a "victim"-must balance two competing strategic interests. Flexibility is valuable because it allows adaptive differentiation in the face of diverse opponents. However, it is also risky because, in competitive games, it can produce systematically suboptimal behaviors. Using a combination of evolutionary analysis, reinforcement learning simulations, and behavioral experimentation, we show that the resolution to this tension-and the adaptation of social behavior in this game-hinges on the game's learning dynamics. Our findings clarify punishment's adaptive basis, offer a case study of the evolution of social preferences, and highlight an important connection between natural selection and learning in the resolution of social conflicts.

Heterogeneous investments promote cooperation in evolutionary public goods games

NASA Astrophysics Data System (ADS)

Wang, Qun; Wang, Hanchen; Zhang, Zhuxi; Li, Yumeng; Liu, Yu; Perc, Matjaž

2018-07-01

The public goods game is widely accepted as a suitable theoretical paradigm for explaining collective cooperation. In this paper, we investigate the impact of heterogeneous investments on cooperation in groups, where the investment of one player to a particular group depends on the fraction of cooperators in that group. Our research reveals that the level of cooperation is significantly promoted as the level of heterogeneity in the investments increases. By studying the payoffs of players at the boundaries of cooperative clusters, we show that the positive effect on the evolution of cooperation can be attributed to the formation of clusters that are more robust against invading defectors. The presented results sharpen our understanding of cooperation in groups that are due to heterogeneity and related asymmetric influences on game dynamics.

Coevolution of game and network structure with adjustable linking

NASA Astrophysics Data System (ADS)

Qin, Shao-Meng; Zhang, Guo-Yong; Chen, Yong

2009-12-01

Most papers about the evolutionary game on graph assume the statistic network structure. However, in the real world, social interaction could change the relationship among people. And the change of social structure will also affect people’s strategies. We build a coevolution model of prisoner’s dilemma game and network structure to study the dynamic interaction in the real world. Differing from other coevolution models, players rewire their network connections according to the density of cooperation and other players’ payoffs. We use a parameter α to control the effect of payoff in the process of rewiring. Based on the asynchronous update rule and Monte Carlo simulation, we find that, when players prefer to rewire their links to those who are richer, the temptation can increase the cooperation density.

Invisible hand effect in an evolutionary minority game model

NASA Astrophysics Data System (ADS)

Sysi-Aho, Marko; Saramäki, Jari; Kaski, Kimmo

2005-03-01

In this paper, we study the properties of a minority game with evolution realized by using genetic crossover to modify fixed-length decision-making strategies of agents. Although the agents in this evolutionary game act selfishly by trying to maximize their own performances only, it turns out that the whole society will eventually be rewarded optimally. This “invisible hand” effect is what Adam Smith over two centuries ago expected to take place in the context of free market mechanism. However, this behaviour of the society of agents is realized only under idealized conditions, where all agents are utilizing the same efficient evolutionary mechanism. If on the other hand part of the agents are adaptive, but not evolutionary, the system does not reach optimum performance, which is also the case if part of the evolutionary agents form a uniformly acting “cartel”.

Evolutionary programming for goal-driven dynamic planning

NASA Astrophysics Data System (ADS)

Vaccaro, James M.; Guest, Clark C.; Ross, David O.

2002-03-01

Many complex artificial intelligence (IA) problems are goal- driven in nature and the opportunity exists to realize the benefits of a goal-oriented solution. In many cases, such as in command and control, a goal-oriented approach may be the only option. One of many appropriate applications for such an approach is War Gaming. War Gaming is an important tool for command and control because it provides a set of alternative courses of actions so that military leaders can contemplate their next move in the battlefield. For instance, when making decisions that save lives, it is necessary to completely understand the consequences of a given order. A goal-oriented approach provides a slowly evolving tractably reasoned solution that inherently follows one of the principles of war: namely concentration on the objective. Future decision-making will depend not only on the battlefield, but also on a virtual world where military leaders can wage wars and determine their options by playing computer war games much like the real world. The problem with these games is that the built-in AI does not learn nor adapt and many times cheats, because the intelligent player has access to all the information, while the user has access to limited information provided on a display. These games are written for the purpose of entertainment and actions are calculated a priori and off-line, and are made prior or during their development. With these games getting more sophisticated in structure and less domain specific in scope, there needs to be a more general intelligent player that can adapt and learn in case the battlefield situations or the rules of engagement change. One such war game that might be considered is Risk. Risk incorporates the principles of war, is a top-down scalable model, and provides a good application for testing a variety of goal- oriented AI approaches. By integrating a goal-oriented hybrid approach, one can develop a program that plays the Risk game effectively and move one step closer to solving more difficult real-world AI problems. Using a hybrid approach that includes adaptation via evolutionary computation for the intelligent planning of a Risk player's turn provides better dynamic intelligent planning than more uniform approaches.

Reinforcement learning in complementarity game and population dynamics

NASA Astrophysics Data System (ADS)

Jost, Jürgen; Li, Wei

2014-02-01

We systematically test and compare different reinforcement learning schemes in a complementarity game [J. Jost and W. Li, Physica A 345, 245 (2005), 10.1016/j.physa.2004.07.005] played between members of two populations. More precisely, we study the Roth-Erev, Bush-Mosteller, and SoftMax reinforcement learning schemes. A modified version of Roth-Erev with a power exponent of 1.5, as opposed to 1 in the standard version, performs best. We also compare these reinforcement learning strategies with evolutionary schemes. This gives insight into aspects like the issue of quick adaptation as opposed to systematic exploration or the role of learning rates.

Cooperation among cancer cells as public goods games on Voronoi networks.

PubMed

Archetti, Marco

2016-05-07

Cancer cells produce growth factors that diffuse and sustain tumour proliferation, a form of cooperation that can be studied using mathematical models of public goods in the framework of evolutionary game theory. Cell populations, however, form heterogeneous networks that cannot be described by regular lattices or scale-free networks, the types of graphs generally used in the study of cooperation. To describe the dynamics of growth factor production in populations of cancer cells, I study public goods games on Voronoi networks, using a range of non-linear benefits that account for the known properties of growth factors, and different types of diffusion gradients. The results are surprisingly similar to those obtained on regular graphs and different from results on scale-free networks, revealing that network heterogeneity per se does not promote cooperation when public goods diffuse beyond one-step neighbours. The exact shape of the diffusion gradient is not crucial, however, whereas the type of non-linear benefit is an essential determinant of the dynamics. Public goods games on Voronoi networks can shed light on intra-tumour heterogeneity, the evolution of resistance to therapies that target growth factors, and new types of cell therapy. Copyright © 2016 Elsevier Ltd. All rights reserved.

Estimating the dilemma strength for game systems. Comment on "Universal scaling for the dilemma strength in evolutionary games", by Z. Wang et al.

NASA Astrophysics Data System (ADS)

Chen, Xiaojie

2015-09-01

The puzzle of cooperation exists widely in the realistic world, including biological, social, and engineering systems. How to solve the cooperation puzzle has received considerable attention in recent years [1]. Evolutionary game theory provides a common mathematical framework to study the problem of cooperation. In principle, these practical biological, social, or engineering systems can be described by complex game models composed of multiple autonomous individuals with mutual interactions. And generally there exists a dilemma for the evolution of cooperation in the game systems.

Entanglement guarantees emergence of cooperation in quantum prisoner's dilemma games on networks.

PubMed

Li, Angsheng; Yong, Xi

2014-09-05

It was known that cooperation of evolutionary prisoner's dilemma games fails to emerge in homogenous networks such as random graphs. Here we proposed a quantum prisoner's dilemma game. The game consists of two players, in which each player has three choices of strategy: cooperator (C), defector (D) and super cooperator (denoted by Q). We found that quantum entanglement guarantees emergence of a new cooperation, the super cooperation of the quantum prisoner's dilemma games, and that entanglement is the mechanism of guaranteed emergence of cooperation of evolutionary prisoner's dilemma games on networks. We showed that for a game with temptation b, there exists a threshold arccos √b/b for a measurement of entanglement, beyond which, (super) cooperation of evolutionary quantum prisoner's dilemma games is guaranteed to quickly emerge, giving rise to stochastic convergence of the cooperations, that if the entanglement degree γ is less than the threshold arccos √b/b, then the equilibrium frequency of cooperations of the games is positively correlated to the entanglement degree γ, and that if γ is less than arccos √b/b and b is beyond some boundary, then the equilibrium frequency of cooperations of the games on random graphs decreases as the average degree of the graphs increases.

A Game-Theoretic Response Strategy for Coordinator Attack in Wireless Sensor Networks

PubMed Central

Liu, Jianhua; Yue, Guangxue; Shang, Huiliang; Li, Hongjie

2014-01-01

The coordinator is a specific node that controls the whole network and has a significant impact on the performance in cooperative multihop ZigBee wireless sensor networks (ZWSNs). However, the malicious node attacks coordinator nodes in an effort to waste the resources and disrupt the operation of the network. Attacking leads to a failure of one round of communication between the source nodes and destination nodes. Coordinator selection is a technique that can considerably defend against attack and reduce the data delivery delay, and increase network performance of cooperative communications. In this paper, we propose an adaptive coordinator selection algorithm using game and fuzzy logic aiming at both minimizing the average number of hops and maximizing network lifetime. The proposed game model consists of two interrelated formulations: a stochastic game for dynamic defense and a best response policy using evolutionary game formulation for coordinator selection. The stable equilibrium best policy to response defense is obtained from this game model. It is shown that the proposed scheme can improve reliability and save energy during the network lifetime with respect to security. PMID:25105171

A game-theoretic response strategy for coordinator attack in wireless sensor networks.

PubMed

Liu, Jianhua; Yue, Guangxue; Shen, Shigen; Shang, Huiliang; Li, Hongjie

2014-01-01

The coordinator is a specific node that controls the whole network and has a significant impact on the performance in cooperative multihop ZigBee wireless sensor networks (ZWSNs). However, the malicious node attacks coordinator nodes in an effort to waste the resources and disrupt the operation of the network. Attacking leads to a failure of one round of communication between the source nodes and destination nodes. Coordinator selection is a technique that can considerably defend against attack and reduce the data delivery delay, and increase network performance of cooperative communications. In this paper, we propose an adaptive coordinator selection algorithm using game and fuzzy logic aiming at both minimizing the average number of hops and maximizing network lifetime. The proposed game model consists of two interrelated formulations: a stochastic game for dynamic defense and a best response policy using evolutionary game formulation for coordinator selection. The stable equilibrium best policy to response defense is obtained from this game model. It is shown that the proposed scheme can improve reliability and save energy during the network lifetime with respect to security.

Analysis of the expected density of internal equilibria in random evolutionary multi-player multi-strategy games.

PubMed

Duong, Manh Hong; Han, The Anh

2016-12-01

In this paper, we study the distribution and behaviour of internal equilibria in a d-player n-strategy random evolutionary game where the game payoff matrix is generated from normal distributions. The study of this paper reveals and exploits interesting connections between evolutionary game theory and random polynomial theory. The main contributions of the paper are some qualitative and quantitative results on the expected density, [Formula: see text], and the expected number, E(n, d), of (stable) internal equilibria. Firstly, we show that in multi-player two-strategy games, they behave asymptotically as [Formula: see text] as d is sufficiently large. Secondly, we prove that they are monotone functions of d. We also make a conjecture for games with more than two strategies. Thirdly, we provide numerical simulations for our analytical results and to support the conjecture. As consequences of our analysis, some qualitative and quantitative results on the distribution of zeros of a random Bernstein polynomial are also obtained.

The dynamics of human behavior in the public goods game with institutional incentives.

PubMed

Dong, Yali; Zhang, Boyu; Tao, Yi

2016-06-24

The empirical research on the public goods game (PGG) indicates that both institutional rewards and institutional punishment can curb free-riding and that the punishment effect is stronger than the reward effect. Self-regarding models that are based on Nash equilibrium (NE) strategies or evolutionary game dynamics correctly predict which incentives are best at promoting cooperation, but individuals do not play these rational strategies overall. The goal of our study is to investigate the dynamics of human decision making in the repeated PGG with institutional incentives. We consider that an individual's contribution is affected by four factors, which are self-interest, the behavior of others, the reaction to rewards, and the reaction to punishment. We find that people on average do not react to rewards and punishment, and that self-interest and the behavior of others sufficiently explain the dynamics of human behavior. Further analysis suggests that institutional incentives promote cooperation by affecting the self-regarding preference and that the other-regarding preference seems to be independent of incentive schemes. Because individuals do not change their behavioral patterns even if they were not rewarded or punished, the mere potential to punish defectors and reward cooperators can lead to considerable increases in the level of cooperation.

The rock-paper-scissors game and the evolution of alternative male strategies

NASA Astrophysics Data System (ADS)

Sinervo, B.; Lively, C. M.

1996-03-01

MANY species exhibit colour polymorphisms associated with alternative male reproductive strategies, including territorial males and 'sneaker males' that behave and look like females1-3. The prevalence of multiple morphs is a challenge to evolutionary theory because a single strategy should prevail unless morphs have exactly equal fitness4,5 or a fitness advantage when rare6,7. We report here the application of an evolutionary stable strategy model to a three-morph mating system in the side-blotched lizard. Using parameter estimates from field data, the model predicted oscillations in morph frequency, and the frequencies of the three male morphs were found to oscillate over a six-year period in the field. The fitnesses of each morph relative to other morphs were non-transitive in that each morph could invade another morph when rare, but was itself invadable by another morph when common. Concordance between frequency-dependent selection and the among-year changes in morph fitnesses suggest that male interactions drive a dynamic 'rock-paper-scissors' game7.

Extrapolating Weak Selection in Evolutionary Games

PubMed Central

Wu, Bin; García, Julián; Hauert, Christoph; Traulsen, Arne

2013-01-01

In evolutionary games, reproductive success is determined by payoffs. Weak selection means that even large differences in game outcomes translate into small fitness differences. Many results have been derived using weak selection approximations, in which perturbation analysis facilitates the derivation of analytical results. Here, we ask whether results derived under weak selection are also qualitatively valid for intermediate and strong selection. By “qualitatively valid” we mean that the ranking of strategies induced by an evolutionary process does not change when the intensity of selection increases. For two-strategy games, we show that the ranking obtained under weak selection cannot be carried over to higher selection intensity if the number of players exceeds two. For games with three (or more) strategies, previous examples for multiplayer games have shown that the ranking of strategies can change with the intensity of selection. In particular, rank changes imply that the most abundant strategy at one intensity of selection can become the least abundant for another. We show that this applies already to pairwise interactions for a broad class of evolutionary processes. Even when both weak and strong selection limits lead to consistent predictions, rank changes can occur for intermediate intensities of selection. To analyze how common such games are, we show numerically that for randomly drawn two-player games with three or more strategies, rank changes frequently occur and their likelihood increases rapidly with the number of strategies . In particular, rank changes are almost certain for , which jeopardizes the predictive power of results derived for weak selection. PMID:24339769

On the complex interplay between learning and dynamics in life sciences. Comment on the paper "Collective learning modeling based on the kinetic theory of active particles" by Burini et al.

NASA Astrophysics Data System (ADS)

Bellomo, Nicola; Elaiw, Ahmed; Alghamdi, Mohamed Ali

2016-03-01

The paper by Burini, De Lillo, and Gibelli [8] presents an overview and critical analysis of the literature on the modeling of learning dynamics. The first reference is the celebrated paper by Cucker and Smale [9]. Then, the authors also propose their own approach, based on suitable development of methods of the kinetic theory [6] and theoretical tools of evolutionary game theory [12,13], recently developed on graphs [2].

Evolutionary games on cycles with strong selection

NASA Astrophysics Data System (ADS)

Altrock, P. M.; Traulsen, A.; Nowak, M. A.

2017-02-01

Evolutionary games on graphs describe how strategic interactions and population structure determine evolutionary success, quantified by the probability that a single mutant takes over a population. Graph structures, compared to the well-mixed case, can act as amplifiers or suppressors of selection by increasing or decreasing the fixation probability of a beneficial mutant. Properties of the associated mean fixation times can be more intricate, especially when selection is strong. The intuition is that fixation of a beneficial mutant happens fast in a dominance game, that fixation takes very long in a coexistence game, and that strong selection eliminates demographic noise. Here we show that these intuitions can be misleading in structured populations. We analyze mean fixation times on the cycle graph under strong frequency-dependent selection for two different microscopic evolutionary update rules (death-birth and birth-death). We establish exact analytical results for fixation times under strong selection and show that there are coexistence games in which fixation occurs in time polynomial in population size. Depending on the underlying game, we observe inherence of demographic noise even under strong selection if the process is driven by random death before selection for birth of an offspring (death-birth update). In contrast, if selection for an offspring occurs before random removal (birth-death update), then strong selection can remove demographic noise almost entirely.

Evolutionary dynamics of cooperation in neutral populations

NASA Astrophysics Data System (ADS)

Szolnoki, Attila; Perc, Matjaž

2018-01-01

Cooperation is a difficult proposition in the face of Darwinian selection. Those that defect have an evolutionary advantage over cooperators who should therefore die out. However, spatial structure enables cooperators to survive through the formation of homogeneous clusters, which is the hallmark of network reciprocity. Here we go beyond this traditional setup and study the spatiotemporal dynamics of cooperation in a population of populations. We use the prisoner's dilemma game as the mathematical model and show that considering several populations simultaneously gives rise to fascinating spatiotemporal dynamics and pattern formation. Even the simplest assumption that strategies between different populations are payoff-neutral with one another results in the spontaneous emergence of cyclic dominance, where defectors of one population become prey of cooperators in the other population, and vice versa. Moreover, if social interactions within different populations are characterized by significantly different temptations to defect, we observe that defectors in the population with the largest temptation counterintuitively vanish the fastest, while cooperators that hang on eventually take over the whole available space. Our results reveal that considering the simultaneous presence of different populations significantly expands the complexity of evolutionary dynamics in structured populations, and it allows us to understand the stability of cooperation under adverse conditions that could never be bridged by network reciprocity alone.

Crucial role of strategy updating for coexistence of strategies in interaction networks.

PubMed

Zhang, Jianlei; Zhang, Chunyan; Cao, Ming; Weissing, Franz J

2015-04-01

Network models are useful tools for studying the dynamics of social interactions in a structured population. After a round of interactions with the players in their local neighborhood, players update their strategy based on the comparison of their own payoff with the payoff of one of their neighbors. Here we show that the assumptions made on strategy updating are of crucial importance for the strategy dynamics. In the first step, we demonstrate that seemingly small deviations from the standard assumptions on updating have major implications for the evolutionary outcome of two cooperation games: cooperation can more easily persist in a Prisoner's Dilemma game, while it can go more easily extinct in a Snowdrift game. To explain these outcomes, we develop a general model for the updating of states in a network that allows us to derive conditions for the steady-state coexistence of states (or strategies). The analysis reveals that coexistence crucially depends on the number of agents consulted for updating. We conclude that updating rules are as important for evolution on a network as network structure and the nature of the interaction.

Crucial role of strategy updating for coexistence of strategies in interaction networks

NASA Astrophysics Data System (ADS)

Zhang, Jianlei; Zhang, Chunyan; Cao, Ming; Weissing, Franz J.

2015-04-01

Network models are useful tools for studying the dynamics of social interactions in a structured population. After a round of interactions with the players in their local neighborhood, players update their strategy based on the comparison of their own payoff with the payoff of one of their neighbors. Here we show that the assumptions made on strategy updating are of crucial importance for the strategy dynamics. In the first step, we demonstrate that seemingly small deviations from the standard assumptions on updating have major implications for the evolutionary outcome of two cooperation games: cooperation can more easily persist in a Prisoner's Dilemma game, while it can go more easily extinct in a Snowdrift game. To explain these outcomes, we develop a general model for the updating of states in a network that allows us to derive conditions for the steady-state coexistence of states (or strategies). The analysis reveals that coexistence crucially depends on the number of agents consulted for updating. We conclude that updating rules are as important for evolution on a network as network structure and the nature of the interaction.

Evolutionary mixed games in structured populations: Cooperation and the benefits of heterogeneity

NASA Astrophysics Data System (ADS)

Amaral, Marco A.; Wardil, Lucas; Perc, Matjaž; da Silva, Jafferson K. L.

2016-04-01

Evolutionary games on networks traditionally involve the same game at each interaction. Here we depart from this assumption by considering mixed games, where the game played at each interaction is drawn uniformly at random from a set of two different games. While in well-mixed populations the random mixture of the two games is always equivalent to the average single game, in structured populations this is not always the case. We show that the outcome is, in fact, strongly dependent on the distance of separation of the two games in the parameter space. Effectively, this distance introduces payoff heterogeneity, and the average game is returned only if the heterogeneity is small. For higher levels of heterogeneity the distance to the average game grows, which often involves the promotion of cooperation. The presented results support preceding research that highlights the favorable role of heterogeneity regardless of its origin, and they also emphasize the importance of the population structure in amplifying facilitators of cooperation.

Evolutionary mixed games in structured populations: Cooperation and the benefits of heterogeneity.

PubMed

Amaral, Marco A; Wardil, Lucas; Perc, Matjaž; da Silva, Jafferson K L

2016-04-01

Evolutionary games on networks traditionally involve the same game at each interaction. Here we depart from this assumption by considering mixed games, where the game played at each interaction is drawn uniformly at random from a set of two different games. While in well-mixed populations the random mixture of the two games is always equivalent to the average single game, in structured populations this is not always the case. We show that the outcome is, in fact, strongly dependent on the distance of separation of the two games in the parameter space. Effectively, this distance introduces payoff heterogeneity, and the average game is returned only if the heterogeneity is small. For higher levels of heterogeneity the distance to the average game grows, which often involves the promotion of cooperation. The presented results support preceding research that highlights the favorable role of heterogeneity regardless of its origin, and they also emphasize the importance of the population structure in amplifying facilitators of cooperation.

Evolutionary dynamics of group formation.

PubMed

Javarone, Marco Alberto; Marinazzo, Daniele

2017-01-01

Group formation is a quite ubiquitous phenomenon across different animal species, whose individuals cluster together forming communities of diverse size. Previous investigations suggest that, in general, this phenomenon might have similar underlying reasons across the interested species, despite genetic and behavioral differences. For instance improving the individual safety (e.g. from predators), and increasing the probability to get food resources. Remarkably, the group size might strongly vary from species to species, e.g. shoals of fishes and herds of lions, and sometimes even within the same species, e.g. tribes and families in human societies. Here we build on previous theories stating that the dynamics of group formation may have evolutionary roots, and we explore this fascinating hypothesis from a purely theoretical perspective, with a model using the framework of Evolutionary Game Theory. In our model we hypothesize that homogeneity constitutes a fundamental ingredient in these dynamics. Accordingly, we study a population that tries to form homogeneous groups, i.e. composed of similar agents. The formation of a group can be interpreted as a strategy. Notably, agents can form a group (receiving a 'group payoff'), or can act individually (receiving an 'individual payoff'). The phase diagram of the modeled population shows a sharp transition between the 'group phase' and the 'individual phase', characterized by a critical 'individual payoff'. Our results then support the hypothesis that the phenomenon of group formation has evolutionary roots.

Predator and prey functional traits: understanding the adaptive machinery driving predator–prey interactions

PubMed Central

Schmitz, Oswald

2017-01-01

Predator–prey relationships are a central component of community dynamics. Classic approaches have tried to understand and predict these relationships in terms of consumptive interactions between predator and prey species, but characterizing the interaction this way is insufficient to predict the complexity and context dependency inherent in predator–prey relationships. Recent approaches have begun to explore predator–prey relationships in terms of an evolutionary-ecological game in which predator and prey adapt to each other through reciprocal interactions involving context-dependent expression of functional traits that influence their biomechanics. Functional traits are defined as any morphological, behavioral, or physiological trait of an organism associated with a biotic interaction. Such traits include predator and prey body size, predator and prey personality, predator hunting mode, prey mobility, prey anti-predator behavior, and prey physiological stress. Here, I discuss recent advances in this functional trait approach. Evidence shows that the nature and strength of many interactions are dependent upon the relative magnitude of predator and prey functional traits. Moreover, trait responses can be triggered by non-consumptive predator–prey interactions elicited by responses of prey to risk of predation. These interactions in turn can have dynamic feedbacks that can change the context of the predator–prey interaction, causing predator and prey to adapt their traits—through phenotypically plastic or rapid evolutionary responses—and the nature of their interaction. Research shows that examining predator–prey interactions through the lens of an adaptive evolutionary-ecological game offers a foundation to explain variety in the nature and strength of predator–prey interactions observed in different ecological contexts. PMID:29043073

Predator and prey functional traits: understanding the adaptive machinery driving predator-prey interactions.

PubMed

Schmitz, Oswald

2017-01-01

Predator-prey relationships are a central component of community dynamics. Classic approaches have tried to understand and predict these relationships in terms of consumptive interactions between predator and prey species, but characterizing the interaction this way is insufficient to predict the complexity and context dependency inherent in predator-prey relationships. Recent approaches have begun to explore predator-prey relationships in terms of an evolutionary-ecological game in which predator and prey adapt to each other through reciprocal interactions involving context-dependent expression of functional traits that influence their biomechanics. Functional traits are defined as any morphological, behavioral, or physiological trait of an organism associated with a biotic interaction. Such traits include predator and prey body size, predator and prey personality, predator hunting mode, prey mobility, prey anti-predator behavior, and prey physiological stress. Here, I discuss recent advances in this functional trait approach. Evidence shows that the nature and strength of many interactions are dependent upon the relative magnitude of predator and prey functional traits. Moreover, trait responses can be triggered by non-consumptive predator-prey interactions elicited by responses of prey to risk of predation. These interactions in turn can have dynamic feedbacks that can change the context of the predator-prey interaction, causing predator and prey to adapt their traits-through phenotypically plastic or rapid evolutionary responses-and the nature of their interaction. Research shows that examining predator-prey interactions through the lens of an adaptive evolutionary-ecological game offers a foundation to explain variety in the nature and strength of predator-prey interactions observed in different ecological contexts.

Phenotype adjustment promotes adaptive evolution in a game without conflict.

PubMed

Yamaguchi, Sachi; Iwasa, Yoh

2015-06-01

Organisms may adjust their phenotypes in response to social and physical environments. Such phenotypic plasticity is known to help or retard adaptive evolution. Here, we study the evolutionary outcomes of adaptive phenotypic plasticity in an evolutionary game involving two players who have no conflicts of interest. A possible example is the growth and sex allocation of a lifelong pair of shrimps entrapped in the body of a sponge. We consider random pair formation, the limitation of total resources for growth, and the needs of male investment to fertilize eggs laid by the partner. We compare the following three different evolutionary dynamics: (1) No adjustment: each individual develops a phenotype specified by its own genotype; (2) One-player adjustment: the phenotype of the first player is specified by its own genotype, and the second player chooses the phenotype that maximizes its own fitness; (3) Two-player adjustment: the first player exhibits an initial phenotype specified by its own genotype, the second player chooses a phenotype given that of the first player, and finally, the first player readjusts its phenotype given that of the second player. We demonstrate that both one-player and two-player adjustments evolve to achieve maximum fitness. In contrast, the dynamics without adjustment fails in some cases to evolve outcomes with the highest fitness. For an intermediate range of male cost, the evolution of no adjustment realizes two hermaphrodites with equal size, whereas the one-player and two-player adjustments realize a small male and a large female. Copyright © 2015 Elsevier Inc. All rights reserved.

Reactive strategies in indirect reciprocity.

PubMed

Ohtsuki, Hisashi

2004-04-07

Evolution of reactive strategy of indirect reciprocity is discussed, where individuals interact with others through the one-shot Prisoner's Dilemma game, changing their partners in every round. We investigate all of the reactive strategies that are stochastic, including deterministic ones as special cases. First we study adaptive dynamics of reactive strategies by assuming monomorphic population. Results are very similar to the corresponding evolutionary dynamics of direct reciprocity. The discriminating strategy, which prescribes cooperation only with those who cooperated in the previous round, cannot be an outcome of the evolution. Next we examine the case where the population includes a diversity of strategies. We find that only the mean 'discriminatoriness' in the population is the parameter that affects the evolutionary dynamics. The discriminating strategy works as a promoter of cooperation there. However, it is again not the end point of the evolution. This is because retaliatory defection, which was prescribed by the discriminating strategy, is regarded as another defection toward the society. These results caution that we have to reconsider the role of retaliatory defection much more carefully.

Statistical physics of the spatial Prisoner's Dilemma with memory-aware agents

NASA Astrophysics Data System (ADS)

Javarone, Marco Alberto

2016-02-01

We introduce an analytical model to study the evolution towards equilibrium in spatial games, with `memory-aware' agents, i.e., agents that accumulate their payoff over time. In particular, we focus our attention on the spatial Prisoner's Dilemma, as it constitutes an emblematic example of a game whose Nash equilibrium is defection. Previous investigations showed that, under opportune conditions, it is possible to reach, in the evolutionary Prisoner's Dilemma, an equilibrium of cooperation. Notably, it seems that mechanisms like motion may lead a population to become cooperative. In the proposed model, we map agents to particles of a gas so that, on varying the system temperature, they randomly move. In doing so, we are able to identify a relation between the temperature and the final equilibrium of the population, explaining how it is possible to break the classical Nash equilibrium in the spatial Prisoner's Dilemma when considering agents able to increase their payoff over time. Moreover, we introduce a formalism to study order-disorder phase transitions in these dynamics. As result, we highlight that the proposed model allows to explain analytically how a population, whose interactions are based on the Prisoner's Dilemma, can reach an equilibrium far from the expected one; opening also the way to define a direct link between evolutionary game theory and statistical physics.

Stochastic evolution in populations of ideas

PubMed Central

Nicole, Robin; Sollich, Peter; Galla, Tobias

2017-01-01

It is known that learning of players who interact in a repeated game can be interpreted as an evolutionary process in a population of ideas. These analogies have so far mostly been established in deterministic models, and memory loss in learning has been seen to act similarly to mutation in evolution. We here propose a representation of reinforcement learning as a stochastic process in finite ‘populations of ideas’. The resulting birth-death dynamics has absorbing states and allows for the extinction or fixation of ideas, marking a key difference to mutation-selection processes in finite populations. We characterize the outcome of evolution in populations of ideas for several classes of symmetric and asymmetric games. PMID:28098244

Stochastic evolution in populations of ideas

NASA Astrophysics Data System (ADS)

Nicole, Robin; Sollich, Peter; Galla, Tobias

2017-01-01

It is known that learning of players who interact in a repeated game can be interpreted as an evolutionary process in a population of ideas. These analogies have so far mostly been established in deterministic models, and memory loss in learning has been seen to act similarly to mutation in evolution. We here propose a representation of reinforcement learning as a stochastic process in finite ‘populations of ideas’. The resulting birth-death dynamics has absorbing states and allows for the extinction or fixation of ideas, marking a key difference to mutation-selection processes in finite populations. We characterize the outcome of evolution in populations of ideas for several classes of symmetric and asymmetric games.

The evolution of fairness through spite

PubMed Central

Forber, Patrick; Smead, Rory

2014-01-01

The presence of apparently irrational fair play in the ultimatum game remains a focal point for studies in the evolution of social behaviour. We investigate the role of negative assortment in the evolution of fair play in the ultimatum game. Spite—social behaviour that inflicts harm with no direct benefit to the actor—can evolve when it is disproportionally directed at individuals playing different strategies. The introduction of negative assortment alters the dynamics in a way that increases the chance fairness evolves, but at a cost: spite also evolves. Fairness is usually linked to cooperation and prosocial behaviour, but this study shows that it may have evolutionary links to harmful antisocial behaviour. PMID:24523265

Spontaneous Symmetry Breaking in Interdependent Networked Game

PubMed Central

Jin, Qing; Wang, Lin; Xia, Cheng-Yi; Wang, Zhen

2014-01-01

Spatial evolution game has traditionally assumed that players interact with direct neighbors on a single network, which is isolated and not influenced by other systems. However, this is not fully consistent with recent research identification that interactions between networks play a crucial rule for the outcome of evolutionary games taking place on them. In this work, we introduce the simple game model into the interdependent networks composed of two networks. By means of imitation dynamics, we display that when the interdependent factor α is smaller than a threshold value αC, the symmetry of cooperation can be guaranteed. Interestingly, as interdependent factor exceeds αC, spontaneous symmetry breaking of fraction of cooperators presents itself between different networks. With respect to the breakage of symmetry, it is induced by asynchronous expansion between heterogeneous strategy couples of both networks, which further enriches the content of spatial reciprocity. Moreover, our results can be well predicted by the strategy-couple pair approximation method. PMID:24526076

Pattern formation, social forces, and diffusion instability in games with success-driven motion

NASA Astrophysics Data System (ADS)

Helbing, Dirk

2009-02-01

A local agglomeration of cooperators can support the survival or spreading of cooperation, even when cooperation is predicted to die out according to the replicator equation, which is often used in evolutionary game theory to study the spreading and disappearance of strategies. In this paper, it is shown that success-driven motion can trigger such local agglomeration and may, therefore, be used to supplement other mechanisms supporting cooperation, like reputation or punishment. Success-driven motion is formulated here as a function of the game-theoretical payoffs. It can change the outcome and dynamics of spatial games dramatically, in particular as it causes attractive or repulsive interaction forces. These forces act when the spatial distributions of strategies are inhomogeneous. However, even when starting with homogeneous initial conditions, small perturbations can trigger large inhomogeneities by a pattern-formation instability, when certain conditions are fulfilled. Here, these instability conditions are studied for the prisoner’s dilemma and the snowdrift game. Furthermore, it is demonstrated that asymmetrical diffusion can drive social, economic, and biological systems into the unstable regime, if these would be stable without diffusion.

The long-term evolution of multilocus traits under frequency-dependent disruptive selection.

PubMed

van Doorn, G Sander; Dieckmann, Ulf

2006-11-01

Frequency-dependent disruptive selection is widely recognized as an important source of genetic variation. Its evolutionary consequences have been extensively studied using phenotypic evolutionary models, based on quantitative genetics, game theory, or adaptive dynamics. However, the genetic assumptions underlying these approaches are highly idealized and, even worse, predict different consequences of frequency-dependent disruptive selection. Population genetic models, by contrast, enable genotypic evolutionary models, but traditionally assume constant fitness values. Only a minority of these models thus addresses frequency-dependent selection, and only a few of these do so in a multilocus context. An inherent limitation of these remaining studies is that they only investigate the short-term maintenance of genetic variation. Consequently, the long-term evolution of multilocus characters under frequency-dependent disruptive selection remains poorly understood. We aim to bridge this gap between phenotypic and genotypic models by studying a multilocus version of Levene's soft-selection model. Individual-based simulations and deterministic approximations based on adaptive dynamics theory provide insights into the underlying evolutionary dynamics. Our analysis uncovers a general pattern of polymorphism formation and collapse, likely to apply to a wide variety of genetic systems: after convergence to a fitness minimum and the subsequent establishment of genetic polymorphism at multiple loci, genetic variation becomes increasingly concentrated on a few loci, until eventually only a single polymorphic locus remains. This evolutionary process combines features observed in quantitative genetics and adaptive dynamics models, and it can be explained as a consequence of changes in the selection regime that are inherent to frequency-dependent disruptive selection. Our findings demonstrate that the potential of frequency-dependent disruptive selection to maintain polygenic variation is considerably smaller than previously expected.

Reconstructing Networks from Profit Sequences in Evolutionary Games via a Multiobjective Optimization Approach with Lasso Initialization

PubMed Central

Wu, Kai; Liu, Jing; Wang, Shuai

2016-01-01

Evolutionary games (EG) model a common type of interactions in various complex, networked, natural and social systems. Given such a system with only profit sequences being available, reconstructing the interacting structure of EG networks is fundamental to understand and control its collective dynamics. Existing approaches used to handle this problem, such as the lasso, a convex optimization method, need a user-defined constant to control the tradeoff between the natural sparsity of networks and measurement error (the difference between observed data and simulated data). However, a shortcoming of these approaches is that it is not easy to determine these key parameters which can maximize the performance. In contrast to these approaches, we first model the EG network reconstruction problem as a multiobjective optimization problem (MOP), and then develop a framework which involves multiobjective evolutionary algorithm (MOEA), followed by solution selection based on knee regions, termed as MOEANet, to solve this MOP. We also design an effective initialization operator based on the lasso for MOEA. We apply the proposed method to reconstruct various types of synthetic and real-world networks, and the results show that our approach is effective to avoid the above parameter selecting problem and can reconstruct EG networks with high accuracy. PMID:27886244

Fixation probabilities of evolutionary coordination games on two coupled populations

NASA Astrophysics Data System (ADS)

Zhang, Liye; Ying, Limin; Zhou, Jie; Guan, Shuguang; Zou, Yong

2016-09-01

Evolutionary forces resulted from competitions between different populations are common, which change the evolutionary behavior of a single population. In an isolated population of coordination games of two strategies (e.g., s1 and s2), the previous studies focused on determining the fixation probability that the system is occupied by only one strategy (s1) and their expectation times, given an initial mixture of two strategies. In this work, we propose a model of two interdependent populations, disclosing the effects of the interaction strength on fixation probabilities. In the well-mixing limit, a detailed linear stability analysis is performed, which allows us to find and to classify the different equilibria, yielding a clear picture of the bifurcation patterns in phase space. We demonstrate that the interactions between populations crucially alter the dynamic behavior. More specifically, if the coupling strength is larger than some threshold value, the critical initial density of one strategy (s1) that corresponds to fixation is significantly delayed. Instead, the two populations evolve to the opposite state of all (s2) strategy, which are in favor of the red queen hypothesis. We delineate the extinction time of strategy (s1) explicitly, which is an exponential form. These results are validated by systematic numerical simulations.

Reconstructing Networks from Profit Sequences in Evolutionary Games via a Multiobjective Optimization Approach with Lasso Initialization

NASA Astrophysics Data System (ADS)

Wu, Kai; Liu, Jing; Wang, Shuai

2016-11-01

Evolutionary games (EG) model a common type of interactions in various complex, networked, natural and social systems. Given such a system with only profit sequences being available, reconstructing the interacting structure of EG networks is fundamental to understand and control its collective dynamics. Existing approaches used to handle this problem, such as the lasso, a convex optimization method, need a user-defined constant to control the tradeoff between the natural sparsity of networks and measurement error (the difference between observed data and simulated data). However, a shortcoming of these approaches is that it is not easy to determine these key parameters which can maximize the performance. In contrast to these approaches, we first model the EG network reconstruction problem as a multiobjective optimization problem (MOP), and then develop a framework which involves multiobjective evolutionary algorithm (MOEA), followed by solution selection based on knee regions, termed as MOEANet, to solve this MOP. We also design an effective initialization operator based on the lasso for MOEA. We apply the proposed method to reconstruct various types of synthetic and real-world networks, and the results show that our approach is effective to avoid the above parameter selecting problem and can reconstruct EG networks with high accuracy.

Examples of equilibrium and non-equilibrium behavior in evolutionary systems

NASA Astrophysics Data System (ADS)

Soulier, Arne

With this thesis, we want to shed some light into the darkness of our understanding of simply defined statistical mechanics systems and the surprisingly complex dynamical behavior they exhibit. We will do so by presenting in turn one equilibrium and then one non-equilibrium system with evolutionary dynamics. In part 1, we will present the seceder-model, a newly developed system that cannot equilibrate. We will then study several properties of the system and obtain an idea of the richness of the dynamics of the seceder model, which is particular impressive given the minimal amount of modeling necessary in its setup. In part 2, we will present extensions to the directed polymer in random media problem on a hypercube and its connection to the Eigen model of evolution. Our main interest will be the influence of time-dependent and time-independent changes in the fitness landscape viewed by an evolving population. This part contains the equilibrium dynamics. The stochastic models and the topic of evolution and non-equilibrium in general will allow us to point out similarities to the various lines of thought in game theory.

Promotion of cooperation by selective group extinction

NASA Astrophysics Data System (ADS)

Böttcher, Marvin A.; Nagler, Jan

2016-06-01

Multilevel selection is an important organizing principle that crucially underlies evolutionary processes from the emergence of cells to eusociality and the economics of nations. Previous studies on multilevel selection assumed that the effective higher-level selection emerges from lower-level reproduction. This leads to selection among groups, although only individuals reproduce. We introduce selective group extinction, where groups die with a probability inversely proportional to their group fitness. When accounting for this the critical benefit-to-cost ratio is substantially lowered. Because in game theory and evolutionary dynamics the degree of cooperation crucially depends on this ratio above which cooperation emerges, previous studies may have substantially underestimated the establishment and maintenance of cooperation.

Evolution Model and Simulation of Profit Model of Agricultural Products Logistics Financing

NASA Astrophysics Data System (ADS)

Yang, Bo; Wu, Yan

2018-03-01

Agricultural products logistics financial warehousing business mainly involves agricultural production and processing enterprises, third-party logistics enterprises and financial institutions tripartite, to enable the three parties to achieve win-win situation, the article first gives the replication dynamics and evolutionary stability strategy between the three parties in business participation, and then use NetLogo simulation platform, using the overall modeling and simulation method of Multi-Agent, established the evolutionary game simulation model, and run the model under different revenue parameters, finally, analyzed the simulation results. To achieve the agricultural products logistics financial financing warehouse business to participate in tripartite mutually beneficial win-win situation, thus promoting the smooth flow of agricultural products logistics business.

Learning dynamics in social dilemmas

PubMed Central

Macy, Michael W.; Flache, Andreas

2002-01-01

The Nash equilibrium, the main solution concept in analytical game theory, cannot make precise predictions about the outcome of repeated mixed-motive games. Nor can it tell us much about the dynamics by which a population of players moves from one equilibrium to another. These limitations, along with concerns about the cognitive demands of forward-looking rationality, have motivated efforts to explore backward-looking alternatives to analytical game theory. Most of the effort has been invested in evolutionary models of population dynamics. We shift attention to a learning-theoretic alternative. Computational experiments with adaptive agents identify a fundamental solution concept for social dilemmas–−stochastic collusion–−based on a random walk from a self-limiting noncooperative equilibrium into a self-reinforcing cooperative equilibrium. However, we show that this solution is viable only within a narrow range of aspiration levels. Below the lower threshold, agents are pulled into a deficient equilibrium that is a stronger attractor than mutual cooperation. Above the upper threshold, agents are dissatisfied with mutual cooperation. Aspirations that adapt with experience (producing habituation to stimuli) do not gravitate into the window of viability; rather, they are the worst of both worlds. Habituation destabilizes cooperation and stabilizes defection. Results from the two-person problem suggest that applications to multiplex and embedded relationships will yield unexpected insights into the global dynamics of cooperation in social dilemmas. PMID:12011402

Analysis of Knowledge-Sharing Evolutionary Game in University Teacher Team

ERIC Educational Resources Information Center

Huo, Mingkui

2013-01-01

The knowledge-sharing activity is a major drive force behind the progress and innovation of university teacher team. Based on the evolutionary game theory, this article analyzes the knowledge-sharing process model of this team, studies the influencing mechanism of various factors such as knowledge aggregate gap, incentive coefficient and risk…

Development of a population of cancer cells: Observation and modeling by a Mixed Spatial Evolutionary Games approach.

PubMed

Świerniak, Andrzej; Krześlak, Michał; Student, Sebastian; Rzeszowska-Wolny, Joanna

2016-09-21

Living cells, like whole living organisms during evolution, communicate with their neighbors, interact with the environment, divide, change their phenotypes, and eventually die. The development of specific ways of communication (through signaling molecules and receptors) allows some cellular subpopulations to survive better, to coordinate their physiological status, and during embryonal development to create tissues and organs or in some conditions to become tumors. Populations of cells cultured in vitro interact similarly, also competing for space and nutrients and stimulating each other to better survive or to die. The results of these intercellular interactions of different types seem to be good examples of biological evolutionary games, and have been the subjects of simulations by the methods of evolutionary game theory where individual cells are treated as players. Here we present examples of intercellular contacts in a population of living human cancer HeLa cells cultured in vitro and propose an evolutionary game theory approach to model the development of such populations. We propose a new technique termed Mixed Spatial Evolutionary Games (MSEG) which are played on multiple lattices corresponding to the possible cellular phenotypes which gives the possibility of simulating and investigating the effects of heterogeneity at the cellular level in addition to the population level. Analyses performed with MSEG suggested different ways in which cellular populations develop in the case of cells communicating directly and through factors released to the environment. Copyright © 2016 Elsevier Ltd. All rights reserved.

Costly Advertising and the Evolution of Cooperation

PubMed Central

Brede, Markus

2013-01-01

In this paper, I investigate the co-evolution of fast and slow strategy spread and game strategies in populations of spatially distributed agents engaged in a one off evolutionary dilemma game. Agents are characterized by a pair of traits, a game strategy (cooperate or defect) and a binary ‘advertising’ strategy (advertise or don’t advertise). Advertising, which comes at a cost , allows investment into faster propagation of the agents’ traits to adjacent individuals. Importantly, game strategy and advertising strategy are subject to the same evolutionary mechanism. Via analytical reasoning and numerical simulations I demonstrate that a range of advertising costs exists, such that the prevalence of cooperation is significantly enhanced through co-evolution. Linking costly replication to the success of cooperators exposes a novel co-evolutionary mechanism that might contribute towards a better understanding of the origins of cooperation-supporting heterogeneity in agent populations. PMID:23861752

Costly advertising and the evolution of cooperation.

PubMed

Brede, Markus

2013-01-01

In this paper, I investigate the co-evolution of fast and slow strategy spread and game strategies in populations of spatially distributed agents engaged in a one off evolutionary dilemma game. Agents are characterized by a pair of traits, a game strategy (cooperate or defect) and a binary 'advertising' strategy (advertise or don't advertise). Advertising, which comes at a cost [Formula: see text], allows investment into faster propagation of the agents' traits to adjacent individuals. Importantly, game strategy and advertising strategy are subject to the same evolutionary mechanism. Via analytical reasoning and numerical simulations I demonstrate that a range of advertising costs exists, such that the prevalence of cooperation is significantly enhanced through co-evolution. Linking costly replication to the success of cooperators exposes a novel co-evolutionary mechanism that might contribute towards a better understanding of the origins of cooperation-supporting heterogeneity in agent populations.

Offspring mortality was a determinant factor in the evolution of paternal investment in humans: An evolutionary game approach.

PubMed

López Alonso, Diego; Ortiz-Rodríguez, Isabel M

2017-04-21

Some researchers support the belief that man evolved philandering behavior because of the greater reproductive success of promiscuous males. According to this idea, deserting behavior from the man should be expected along with null paternal involvement in offspring care. Paradoxically however, the average offspring investment in the human male is far higher than that of any other male mammal, including other primates. In our work, we have addressed this conundrum by employing evolutionary game theory, using objective payoffs instead of, as are commonly used, arbitrary payoffs. Payoffs were computed as reproductive successes by a model based on trivial probabilities, implemented within the Barreto's Population Dynamics Toolbox (2014). The evolution of the parent conflict was simulated by a game with two players (the woman and the man). First, a simple game was assayed with two strategies, 'desert-unfaithful' and 'care-faithful'. Then, the game was played with a third mixed strategy, 'care-unfaithful'. The two-strategy game results were mainly determined by the offspring survival rate (s) and the non-paternity rate (z), with remaining factors playing a secondary role. Starting from two empirical estimates for both rates (s = 0.617 and z = 0.033) and decreasing the offspring mortality from near 0.4 to 0.1, the results were consistent with a win for the 'care-faithful' strategy. The 'desert-unfaithful' strategy only won at unrealistically high non-paternity rates (z>0.2). When three-strategy games were played, the mixed strategy of 'care-unfaithful' man could win the game in some less frequent cases. Regardless of the number of game strategies, 'care' fathers always won. These results strongly suggest that offspring mortality was the key factor in the evolution of paternal investment within the Homo branch. The 'care-faithful' strategy would have been the main strategy in human evolution but 'care-unfaithful' men did evolve at a lesser frequency. It can therefore be concluded that human populations, under most of the likely ecological situations, would arrive at a polymorphic state where alternative strategies might be present in significant quantity. Copyright © 2017 Elsevier Ltd. All rights reserved.

Effect of self-interaction on the evolution of cooperation in complex topologies

NASA Astrophysics Data System (ADS)

Wu, Yu'e.; Zhang, Zhipeng; Chang, Shuhua

2017-09-01

Self-interaction, as a significant mechanism explaining the evolution of cooperation, has attracted great attention both theoretically and experimentally. In this text, we consider a new self-interaction mechanism in the two typical pairwise models including the prisoner's dilemma and the snowdrift games, where the cooperative agents will gain extra bonus for their selfless behavior. We find that under the mechanism the collective cooperation is elevated to a very high level especially after adopting the finite population analogue of replicator dynamics for evolution. The robustness of the new mechanism is tested for different complex topologies for the prisoner's dilemma game. All the presented results demonstrate that the enhancement effects are independent of the structure of the applied spatial networks and the potential evolutionary games, and thus showing a high degree of universality. Our conclusions might shed light on the understanding of the evolution of cooperation in the real world.

Fairness emergence from zero-intelligence agents

NASA Astrophysics Data System (ADS)

Duan, Wen-Qi; Stanley, H. Eugene

2010-02-01

Fairness plays a key role in explaining the emergence and maintenance of cooperation. Opponent-oriented social utility models were often proposed to explain the origins of fairness preferences in which agents take into account not only their own outcomes but are also concerned with the outcomes of their opponents. Here, we propose a payoff-oriented mechanism in which agents update their beliefs only based on the payoff signals of the previous ultimatum game, regardless of the behaviors and outcomes of the opponents themselves. Employing adaptive ultimatum game, we show that (1) fairness behaviors can emerge out even under such minimalist assumptions, provided that agents are capable of responding to their payoff signals, (2) the average game payoff per agent per round decreases with the increasing discrepancy rate between the average giving rate and the average asking rate, and (3) the belief update process will lead to 50%-50% fair split provided that there is no mutation in the evolutionary dynamics.

Despotism, democracy, and the evolutionary dynamics of leadership and followership.

PubMed

Van Vugt, Mark

2009-01-01

Responds to comments made by George B. Graen and Stephen J. Guastello on the current author's article Leadership, followership, and evolution: Some lessons from the past by Van Vugt, Hogan, and Kaiser. In the original article my co-authors and I proposed a new way of thinking about leadership, informed by evolutionary (neo-Darwinian) theory. In the first commentary, Graen noted that we ignored a number of recently developed psychological theories of leadership that take into account the leader-follower relationship, most notably LMX theory. LMX theory asserts that leadership effectiveness and team performance are affected by the quality of working relationships between superior and subordinates. Because the original article primarily dealt with questions about the origins of leadership--the phylogenetic and evolutionary causes--we had to be concise in our review of proximate psychological theories of leadership. In the second commentary, Guastello concurred with the importance of an evolutionary game analysis for studying leadership but disagreed with certain details of our analysis. (PsycINFO Database Record (c) 2009 APA, all rights reserved).

Use of game-theoretical methods in biochemistry and biophysics.

PubMed

Schuster, Stefan; Kreft, Jan-Ulrich; Schroeter, Anja; Pfeiffer, Thomas

2008-04-01

Evolutionary game theory can be considered as an extension of the theory of evolutionary optimisation in that two or more organisms (or more generally, units of replication) tend to optimise their properties in an interdependent way. Thus, the outcome of the strategy adopted by one species (e.g., as a result of mutation and selection) depends on the strategy adopted by the other species. In this review, the use of evolutionary game theory for analysing biochemical and biophysical systems is discussed. The presentation is illustrated by a number of instructive examples such as the competition between microorganisms using different metabolic pathways for adenosine triphosphate production, the secretion of extracellular enzymes, the growth of trees and photosynthesis. These examples show that, due to conflicts of interest, the global optimum (in the sense of being the best solution for the whole system) is not always obtained. For example, some yeast species use metabolic pathways that waste nutrients, and in a dense tree canopy, trees grow taller than would be optimal for biomass productivity. From the viewpoint of game theory, the examples considered can be described by the Prisoner's Dilemma, snowdrift game, Tragedy of the Commons and rock-scissors-paper game.

Evolutionary game theory and multiple chemical sensitivity.

PubMed

Newlin, D B

1999-01-01

Newlin's [Newlin D.B. Evolutionary game theory of tolerance and sensitization in substance abuse. Paper presented to the Research Society on Alcoholism, Hilton Head, SC, 1998] evolutionary game theory of addictive behavior specifies how evolutionarily stable strategies for survival and reproduction may lead to addiction. The game theory of multiple chemical sensitivity (MCS) assumes that: (1) the MCS patient responds to low-level toxicants as stressors or as direct threats to their survival and reproductive fitness, (2) this activates the cortico-mesolimbic dopamine system, (3) this system is a survival motivation center--not a 'reward center', (4) the subject emits a counter-response that is in the same direction as the naive response to the chemicals, (5) previously neutral stimuli associated with chemicals also trigger conditioned responses that mimic those to the chemicals, (6) these counter-responses further activate the dopaminergic survival motivation system, and (7) this produces a positive feedback loop that leads to strong neural sensitization in these structures and in behavior controlled by this system, despite a small initial response. Psychologically, the MCS patient with a sensitized cortico-mesolimbic dopamine system is behaving as though his/her survival is directly threatened by these chemicals. Non-MCS subjects have counter-responses opposite in direction to those of the chemicals and show tolerance. An autoshaping/sign-tracking model of this game is discussed. This evolutionary game makes several specific, testable predictions about differences between MCS subjects, non-MCS controls, and substance abusers in laboratory experiments, and between sensitized and nonsensitized animals.

Memory boosts turn taking in evolutionary dilemma games.

PubMed

Wang, Tao; Chen, Zhigang; Yang, Lei; Zou, You; Luo, Juan

2015-05-01

Spontaneous turn taking phenomenon can be observed in many self-organized systems, and the mechanism is unclear. This paper tries to model it by evolutionary dilemma games with memory mechanism. Prisoner's dilemma, Snowdrift (including Leader and Hero) and Stag-hunt games are unified on an extended S-T plane. Agents play game with all the others and make decision by the last game histories. The experiments find that when agents remember last 2-step histories or more, a kind of cooperative turn taking (CAD) bursts at the area of Snowdrift game with restriction of S + T > 2R and S ≠ T, while the consistent strategy (DorC) gathers on the line of S + T > 2R and S = T. We also find that the system's fitness ratio greatly improved with 2-step memory. Copyright © 2015 Elsevier Ireland Ltd. All rights reserved.

Spiraling patterns in evolutionary models inspired by bacterial games with cyclic dominance

NASA Astrophysics Data System (ADS)

Mobilia, Mauro

2015-03-01

Understanding the mechanisms allowing the maintenance of biodiversity is a central issue in biology. Evolutionary game theory, where the success of one species depends on what the others are doing, provides a promising framework to investigate this complex problem. Experiments on microbial populations have shown that cyclic local interactions promote species coexistence. In this context, rock-paper-scissors games - in which rock crushes scissors, scissors cut paper, and paper wraps rock - are often used to model the dynamics of populations in cyclic competition. After a brief survey of some inspiring experiments, I will discuss the subtle interplay between individuals' mobility and their local interactions in two-dimensional rock-paper-scissors systems. This leads to the loss of biodiversity above a certain mobility threshold, and to the formation of spiraling patterns below the critical mobility rate. I will then study a generic rock-paper-scissors metapopulation model formulated on a two-dimensional grid of patches. When these have a large carrying capacity, the model's dynamics is faithfully described in terms of the system's complex Ginzburg-Landau equation properly derived from a multiscale expansion. The properties of the ensuing complex Ginzburg-Landau equation are exploited to derive the system's phase diagram and to characterize the spatio-temporal properties of the spiraling patterns in each phase. This enables us to analyze the spiral waves stability, how these are influenced by linear and nonlinear diffusion, and to discuss phenomena such as far-field breakup. Presentation mainy based on joint work with B. Szczesny and A. M. Rucklidge. Fruitful earlier collaborations with E. Frey, Q. He, T. Reichenbach, and U. C. Täuber are also acknowledged. Work supported by the UK EPSRC (Grant No. EP/P505593/1).

Evolution of fairness and coalition formation in three-person ultimatum games.

PubMed

Nishimura, Takeshi; Okada, Akira; Shirata, Yasuhiro

2017-05-07

We consider the evolution of fairness and coalition formation in a three-person ultimatum game in which the coalition value depends on its size. Traditional game theory, which assumes selfish and rational players, predicts the largest and efficient coalition with a proposer exploiting most of the total value. In a stochastic evolutionary model (the frequency-dependent Moran process with mutations) where players make errors in estimating the payoffs and strategies of others, evolutionary selection favors the formation of a two-person subcoalition under weak selection and in the low mutation limit if and only if its coalition value exceeds a high proportion (0.7) of that of the largest coalition. Proposers offer 30-35% of the subcoalition value to a coalition member, excluding a non-member. Multilateral bargaining is critically different from the bilateral one. Coalition-forming behavior may cause economic inefficiency and social exclusion. Stochastic evolutionary game theory thus provides theoretical support to explain the behavior of human subjects in economic experiments of a three-person ultimatum game. Copyright © 2017 Elsevier Ltd. All rights reserved.

Intelligent tit-for-tat in the iterated prisoner's dilemma game

NASA Astrophysics Data System (ADS)

Baek, Seung Ki; Kim, Beom Jun

2008-07-01

We seek a route to the equilibrium where all the agents cooperate in the iterated prisoner’s dilemma game on a two-dimensional plane, focusing on the role of tit-for-tat strategy. When a time horizon, within which a strategy can recall the past, is one time step, an equilibrium can be achieved as cooperating strategies dominate the whole population via proliferation of tit-for-tat. Extending the time horizon, we filter out poor strategies by simplified replicator dynamics and observe a similar evolutionary pattern to reach the cooperating equilibrium. In particular, the rise of a modified tit-for-tat strategy plays a central role, which implies how a robust strategy is adopted when provided with an enhanced memory capacity.

Information visualization of the minority game

NASA Astrophysics Data System (ADS)

Jiang, W.; Herbert, R. D.; Webber, R.

2008-02-01

Many dynamical systems produce large quantities of data. How can the system be understood from the output data? Often people are simply overwhelmed by the data. Traditional tools such as tables and plots are often not adequate, and new techniques are needed to help people to analyze the system. In this paper, we propose the use of two spacefilling visualization tools to examine the output from a complex agent-based financial model. We measure the effectiveness and performance of these tools through usability experiments. Based on the experimental results, we develop two new visualization techniques that combine the advantages and discard the disadvantages of the information visualization tools. The model we use is an evolutionary version of the Minority Game which simulates a financial market.

Inactivation of tumor suppressor genes and cancer therapy: An evolutionary game theory approach.

PubMed

Khadem, Heydar; Kebriaei, Hamed; Veisi, Zahra

2017-06-01

Inactivation of alleles in tumor suppressor genes (TSG) is one of the important issues resulting in evolution of cancerous cells. In this paper, the evolution of healthy, one and two missed allele cells is modeled using the concept of evolutionary game theory and replicator dynamics. The proposed model also takes into account the interaction rates of the cells as designing parameters of the system. Different combinations of the equilibrium points of the parameterized nonlinear system is studied and categorized into some cases. In each case, the interaction rates' values are suggested in a way that the equilibrium points of the replicator dynamics are located on an appropriate region of the state space. Based on the suggested interaction rates, it is proved that the system doesn't have any undesirable interior equilibrium point as well. Therefore, the system will converge to the desirable region, where there is a scanty level of cancerous cells. In addition, the proposed conditions for interaction rates guarantee that, when a trajectory of the system reaches the boundaries, then it will stay there forever which is a desirable property since the equilibrium points have been already located on the boundaries, appropriately. The simulation results show the effectiveness of the suggestions in the elimination of the cancerous cells in different scenarios. Copyright © 2017 Elsevier Inc. All rights reserved.

Social dilemmas in multistrategy evolutionary potential games

NASA Astrophysics Data System (ADS)

Szabó, György; Bunth, Gergely

2018-01-01

The nature of social dilemmas is studied in n -strategy evolutionary potential games on a square lattice with nearest-neighbor interactions and the logit rule. For symmetric games with symmetric payoff matrices there are no dilemmas because of the coincidence of individual and common interests. The dilemmas are caused by the antisymmetric parts of the self- and cross-dependent payoff components if it modifies the preferred Nash equilibrium. The contentment of players and the emergence of dilemmas in the preferred Nash equilibria are illustrated on some two-dimensional cross sections of the parameter space.

Multidimensional extended spatial evolutionary games.

PubMed

Krześlak, Michał; Świerniak, Andrzej

2016-02-01

The goal of this paper is to study the classical hawk-dove model using mixed spatial evolutionary games (MSEG). In these games, played on a lattice, an additional spatial layer is introduced for dependence on more complex parameters and simulation of changes in the environment. Furthermore, diverse polymorphic equilibrium points dependent on cell reproduction, model parameters, and their simulation are discussed. Our analysis demonstrates the sensitivity properties of MSEGs and possibilities for further development. We discuss applications of MSEGs, particularly algorithms for modelling cell interactions during the development of tumours. Copyright © 2015 Elsevier Ltd. All rights reserved.

Cancer treatment scheduling and dynamic heterogeneity in social dilemmas of tumour acidity and vasculature.

PubMed

Kaznatcheev, Artem; Vander Velde, Robert; Scott, Jacob G; Basanta, David

2017-03-14

Tumours are diverse ecosystems with persistent heterogeneity in various cancer hallmarks like self-sufficiency of growth factor production for angiogenesis and reprogramming of energy metabolism for aerobic glycolysis. This heterogeneity has consequences for diagnosis, treatment and disease progression. We introduce the double goods game to study the dynamics of these traits using evolutionary game theory. We model glycolytic acid production as a public good for all tumour cells and oxygen from vascularisation via vascular endothelial growth factor production as a club good benefiting non-glycolytic tumour cells. This results in three viable phenotypic strategies: glycolytic, angiogenic and aerobic non-angiogenic. We classify the dynamics into three qualitatively distinct regimes: (1) fully glycolytic; (2) fully angiogenic; or (3) polyclonal in all three cell types. The third regime allows for dynamic heterogeneity even with linear goods, something that was not possible in prior public good models that considered glycolysis or growth factor production in isolation. The cyclic dynamics of the polyclonal regime stress the importance of timing for anti-glycolysis treatments like lonidamine. The existence of qualitatively different dynamic regimes highlights the order effects of treatments. In particular, we consider the potential of vascular normalisation as a neoadjuvant therapy before follow-up with interventions like buffer therapy.

Co-evolutionary data mining for fuzzy rules: automatic fitness function creation phase space, and experiments

NASA Astrophysics Data System (ADS)

Smith, James F., III; Blank, Joseph A.

2003-03-01

An approach is being explored that involves embedding a fuzzy logic based resource manager in an electronic game environment. Game agents can function under their own autonomous logic or human control. This approach automates the data mining problem. The game automatically creates a cleansed database reflecting the domain expert's knowledge, it calls a data mining function, a genetic algorithm, for data mining of the data base as required and allows easy evaluation of the information extracted. The co-evolutionary fitness functions, chromosomes and stopping criteria for ending the game are discussed. Genetic algorithm and genetic program based data mining procedures are discussed that automatically discover new fuzzy rules and strategies. The strategy tree concept and its relationship to co-evolutionary data mining are examined as well as the associated phase space representation of fuzzy concepts. The overlap of fuzzy concepts in phase space reduces the effective strategies available to adversaries. Co-evolutionary data mining alters the geometric properties of the overlap region known as the admissible region of phase space significantly enhancing the performance of the resource manager. Procedures for validation of the information data mined are discussed and significant experimental results provided.

A novel framework of classical and quantum prisoner's dilemma games on coupled networks.

PubMed

Deng, Xinyang; Zhang, Qi; Deng, Yong; Wang, Zhen

2016-03-15

Evolutionary games on multilayer networks are attracting growing interest. While among previous studies, the role of quantum games in such a infrastructure is still virgin and may become a fascinating issue across a myriad of research realms. To mimick two kinds of different interactive environments and mechanisms, in this paper a new framework of classical and quantum prisoner's dilemma games on two-layer coupled networks is considered. Within the proposed model, the impact of coupling factor of networks and entanglement degree in quantum games on the evolutionary process has been studied. Simulation results show that the entanglement has no impact on the evolution of the classical prisoner's dilemma, while the rise of the coupling factor obviously impedes cooperation in this game, and the evolution of quantum prisoner's dilemma is greatly impacted by the combined effect of entanglement and coupling.

A novel framework of classical and quantum prisoner’s dilemma games on coupled networks

PubMed Central

Deng, Xinyang; Zhang, Qi; Deng, Yong; Wang, Zhen

2016-01-01

Evolutionary games on multilayer networks are attracting growing interest. While among previous studies, the role of quantum games in such a infrastructure is still virgin and may become a fascinating issue across a myriad of research realms. To mimick two kinds of different interactive environments and mechanisms, in this paper a new framework of classical and quantum prisoner’s dilemma games on two-layer coupled networks is considered. Within the proposed model, the impact of coupling factor of networks and entanglement degree in quantum games on the evolutionary process has been studied. Simulation results show that the entanglement has no impact on the evolution of the classical prisoner’s dilemma, while the rise of the coupling factor obviously impedes cooperation in this game, and the evolution of quantum prisoner’s dilemma is greatly impacted by the combined effect of entanglement and coupling. PMID:26975447

Evolutionary Games of Multiplayer Cooperation on Graphs

PubMed Central

Arranz, Jordi; Traulsen, Arne

2016-01-01

There has been much interest in studying evolutionary games in structured populations, often modeled as graphs. However, most analytical results so far have only been obtained for two-player or linear games, while the study of more complex multiplayer games has been usually tackled by computer simulations. Here we investigate evolutionary multiplayer games on graphs updated with a Moran death-Birth process. For cycles, we obtain an exact analytical condition for cooperation to be favored by natural selection, given in terms of the payoffs of the game and a set of structure coefficients. For regular graphs of degree three and larger, we estimate this condition using a combination of pair approximation and diffusion approximation. For a large class of cooperation games, our approximations suggest that graph-structured populations are stronger promoters of cooperation than populations lacking spatial structure. Computer simulations validate our analytical approximations for random regular graphs and cycles, but show systematic differences for graphs with many loops such as lattices. In particular, our simulation results show that these kinds of graphs can even lead to more stringent conditions for the evolution of cooperation than well-mixed populations. Overall, we provide evidence suggesting that the complexity arising from many-player interactions and spatial structure can be captured by pair approximation in the case of random graphs, but that it need to be handled with care for graphs with high clustering. PMID:27513946

The law of cooperation: Comment on "Universal scaling for the dilemma strength in evolutionary games" by Z. Wang et al.

NASA Astrophysics Data System (ADS)

Ichinose, Genki

2015-09-01

Cooperation is a behavior that benefits others while incurring costs to the actor. Thus, natural selection favors defection (non-cooperation), which unilaterally takes the benefits without paying any costs, rather than cooperation. Despite this logical consequence, reality is the opposite: Cooperation is ubiquitous at any level from genomes to human societies. This contradiction is known as the puzzle of the evolution of cooperation. For a long time, evolutionary game theorists have used the prisoner's dilemma game (PD) and the chicken game (CH) as the standard models to solve this puzzle. For these researchers, it is recognized that a specific mechanism is needed for the evolution of cooperation [1]. Five mechanisms are proposed: kin selection, direct reciprocity, indirect reciprocity, network reciprocity, and group selection. By using the donor and recipient game (D&R), which is one of the particular forms of PD, Nowak theoretically showed that once benefit (b), cost (c), and the other one or two parameters for each mechanism are given, we (evolutionary game theorists) can immediately know whether cooperation evolves [1]. The point here is that he included those unique parameters for each mechanism into PD and then reformulated the payoff matrix. Therefore, we can use this extended PD as the first scaling parameters.

An IUR evolutionary game model on the patent cooperate of Shandong China

NASA Astrophysics Data System (ADS)

Liu, Mengmeng; Ma, Yinghong; Liu, Zhiyuan; You, Xuemei

2017-06-01

Organizations of industries and university & research institutes cooperate to meet their respective needs based on social contacts, trust and share complementary resources. From the perspective of complex network together with the patent data of Shandong province in China, a novel evolutionary game model on patent cooperation network is presented. Two sides in the game model are industries and universities & research institutes respectively. The cooperation is represented by a connection when a new patent is developed together by the two sides. The optimal strategy of the evolutionary game model is quantified by the average positive cooperation probability p ¯ and the average payoff U ¯ . The feasibility of this game model is simulated on the parameters such as the knowledge spillover, the punishment, the development cost and the distribution coefficient of the benefit. The numerical simulations show that the cooperative behaviors are affected by the variation of parameters. The knowledge spillover displays different behaviors when the punishment is larger than the development cost or less than it. Those results indicate that reasonable punishment would improve the positive cooperation. The appropriate punishment will be useful to enhance the big degree nodes positively cooperate with industries and universities & research institutes. And an equitable plan for the distribution of cooperative profits is half-and-half distribution strategy for the two sides in game.

Dynamic instability of cooperation due to diverse activity patterns in evolutionary social dilemmas

NASA Astrophysics Data System (ADS)

Xia, Cheng-Yi; Meloni, Sandro; Perc, Matjaž; Moreno, Yamir

2015-03-01

Individuals might abstain from participating in an instance of an evolutionary game for various reasons, ranging from lack of interest to risk aversion. In order to understand the consequences of such diverse activity patterns on the evolution of cooperation, we study a weak prisoner's dilemma where each player's participation is probabilistic rather than certain. Players that do not participate get a null payoff and are unable to replicate. We show that inactivity introduces cascading failures of cooperation, which are particularly severe on scale-free networks with frequently inactive hubs. The drops in the fraction of cooperators are sudden, while the spatiotemporal reorganization of compact cooperative clusters, and thus the recovery, takes time. Nevertheless, if the activity of players is directly proportional to their degree, or if the interaction network is not strongly heterogeneous, the overall evolution of cooperation is not impaired. This is because inactivity negatively affects the potency of low-degree defectors, who are hence unable to utilize on their inherent evolutionary advantage. Between cascading failures, the fraction of cooperators is therefore higher than usual, which lastly balances out the asymmetric dynamic instabilities that emerge due to intermittent blackouts of cooperative hubs.

Evolutionary dynamics of nationalism and migration

NASA Astrophysics Data System (ADS)

Barreira da Silva Rocha, André

2013-08-01

I present a dynamic evolutionary game model to address the relation between nationalism against immigrants and assimilation of the latter into the host country culture. I assume a country composed of two different large polymorphic populations, one of native citizens and the other of immigrants. A native citizen may behave nationalistically or may welcome immigrants. Immigrants may have an interest in learning the host country language or not. Evolution is modeled using replicator dynamics (RD). I also account for the presence of an enclave of immigrants in the host country. In the RD, the latter represents the immigrants’ own population effect, which contribution to fitness is controlled using a parameter ρ, 0≤ρ≤1, that represents the enclave size. In line with the empirical literature on migration, the existence of an enclave of immigrants makes assimilation less likely to occur. For large values of ρ, complete assimilation may not occur even if immigrants and natives share very close cultures and norms. Government policy regarding nationalism is modeled both exogenously and endogenously. A single or multiple asymptotically stable states exist for all cases studied but one in which the dynamics is similar to that found in the predator-prey model of Lotka-Volterra for competing species.

Dynamic phase transition in the prisoner's dilemma on a lattice with stochastic modifications

NASA Astrophysics Data System (ADS)

Saif, M. Ali; Gade, Prashant M.

2010-03-01

We present a detailed study of the prisoner's dilemma game with stochastic modifications on a two-dimensional lattice, in the presence of evolutionary dynamics. By very nature of the rules, the cooperators have incentives to cheat and fear being cheated. They may cheat even when this is not dictated by the evolutionary dynamics. We consider two variants here. In each case, the agents mimic the action (cooperation or defection) in the previous time step of the most successful agent in the neighborhood. But over and above this, the fraction p of cooperators spontaneously change their strategy to pure defector at every time step in the first variant. In the second variant, there are no pure cooperators. All cooperators keep defecting with probability p at every time step. In both cases, the system switches from a coexistence state to an all-defector state for higher values of p. We show that the transition between these states unambiguously belongs to the directed percolation universality class in 2 + 1 dimensions. We also study the local persistence. The persistence exponents obtained are higher than the ones obtained in previous studies, underlining their dependence on details of the dynamics.

Topology Property and Dynamic Behavior of a Growing Spatial Network

NASA Astrophysics Data System (ADS)

Cao, Xian-Bin; Du, Wen-Bo; Hu, Mao-Bin; Rong, Zhi-Hai; Sun, Peng; Chen, Cai-Long

In this paper, we propose a growing spatial network (GSN) model and investigate its topology properties and dynamical behaviors. The model is generated by adding one node i with m links into a square lattice at each time step and the new node i is connected to the existing nodes with probabilities proportional to: ({kj})α /dij2, where kj is the degree of node j, α is the tunable parameter and dij is the Euclidean distance between i and j. It is found that both the degree heterogeneity and the clustering coefficient monotonously increase with the increment of α, while the average shortest path length monotonously decreases. Moreover, the evolutionary game dynamics and network traffic dynamics are investigated. Simulation results show that the value of α can also greatly influence the dynamic behaviors.

Structure coefficients and strategy selection in multiplayer games.

PubMed

McAvoy, Alex; Hauert, Christoph

2016-01-01

Evolutionary processes based on two-player games such as the Prisoner's Dilemma or Snowdrift Game are abundant in evolutionary game theory. These processes, including those based on games with more than two strategies, have been studied extensively under the assumption that selection is weak. However, games involving more than two players have not received the same level of attention. To address this issue, and to relate two-player games to multiplayer games, we introduce a notion of reducibility for multiplayer games that captures what it means to break down a multiplayer game into a sequence of interactions with fewer players. We discuss the role of reducibility in structured populations, and we give examples of games that are irreducible in any population structure. Since the known conditions for strategy selection, otherwise known as [Formula: see text]-rules, have been established only for two-player games with multiple strategies and for multiplayer games with two strategies, we extend these rules to multiplayer games with many strategies to account for irreducible games that cannot be reduced to those simpler types of games. In particular, we show that the number of structure coefficients required for a symmetric game with [Formula: see text]-player interactions and [Formula: see text] strategies grows in [Formula: see text] like [Formula: see text]. Our results also cover a type of ecologically asymmetric game based on payoff values that are derived not only from the strategies of the players, but also from their spatial positions within the population.

Evolutionary Game Model Study of Construction Green Supply Chain Management under the Government Intervention

NASA Astrophysics Data System (ADS)

Xing, Yuanzhi; Deng, Xiaoyi

2017-11-01

The paper first has defined the concepts of green supply chain management and evolution game theory, and pointed out the characteristics of green supply chain management in construction. The main participants and key links of the construction green supply chain management are determined by constructing the organization framework. This paper established the evolutionary game model between construction enterprises and recycling enterprises for the green supply chain closed-loop structure. The waste recycling evolutionary stability equilibrium solution is obtained to explore the principle and effective scope of government policy intervention. This paper put forward the relevant countermeasures to the green supply chain management in construction recycling stage from the government point of view. The conclusion has reference value and guidance to the final product construction enterprises, recycling enterprises and the government during green supply chain.

Strategic interactions: Games of the Ju|'hoan.

PubMed

de Voogt, Alex

2017-12-01

Three strategic games played by the Ju|'hoan-a board, a card, and a gesture game-complicate the rhetorics that suggest an evolutionary or psychological significance of play. They are mostly played by adults, although every individual adult does not necessarily engage in each game. The Ju|'hoan card and board game practices were transmitted through contact across large parts of Botswana and Namibia, while the gesture game n!àì has been known in other San communities. It suggests that the significance of strategic games is more likely found in its potential for social interaction (i.e., allowing to overcome cultural divides) than in evolution and psychology. Within the anthropological literature, strategy games were thought to be absent in egalitarian societies, such as that of the Ju|'hoan. Here, the roles of power, competition, and winning were thought to be disruptive and unwanted. A closer examination of the details behind the Ju|'hoan games shows that not only were strategy games adopted and adapted from neighboring societies but that the game of n!àì was developed by the Ju|'hoan into a competitive one. The evolutionary or psychological significance of play is informed by studies on individual play, children's play, and games with informal rules. When considering strategic games throughout history, it is their role of facilitator rather than the playing practice itself that makes games relevant across languages, cultural divides, and sociopolitical boundaries.

Evolutionary dynamics under interactive diversity

NASA Astrophysics Data System (ADS)

Su, Qi; Li, Aming; Wang, Long

2017-10-01

As evidenced by many cases in human societies, individuals often make different behavior decisions in different interactions, and adaptively adjust their behavior in changeable interactive scenarios. However, up to now, how such diverse interactive behavior affects cooperation dynamics has still remained unknown. Here we develop a general framework of interactive diversity, which models individuals’ separated behavior against distinct opponents and their adaptive adjustment in response to opponents’ strategies, to explore the evolution of cooperation. We find that interactive diversity enables individuals to reciprocate every single opponent, and thus sustains large-scale reciprocal interactions. Our work witnesses an impressive boost of cooperation for a notably extensive range of parameters and for all pairwise games. These results are robust against well-mixed and various networked populations, and against degree-normalized and cumulative payoff patterns. From the perspective of network dynamics, distinguished from individuals competing for nodes in most previous work, in this paper, the system evolves in the form of behavior disseminating along edges. We propose a theoretical method based on evolution of edges, which predicts well both the frequency of cooperation and the compact cooperation clusters. Our thorough investigation clarifies the positive role of interactive diversity in resolving social dilemmas and highlights the significance of understanding evolutionary dynamics from the viewpoint of edge dynamics.

Chaos and the evolution of cooperation.

PubMed

Nowak, M; Sigmund, K

1993-06-01

The "iterated prisoner's dilemma" is the most widely used model for the evolution of cooperation in biological societies. Here we show that a heterogeneous population consisting of simple strategies, whose behavior is totally specified by the outcome of the previous round, can lead to persistent periodic or highly irregular (chaotic) oscillations in the frequencies of the strategies and the overall level of cooperation. The levels of cooperation jump up and down in an apparently unpredictable fashion. Small recurrent and simultaneous invasion attempts (caused by mutation) can change the evolutionary dynamics from converging to an evolutionarily stable strategy to periodic oscillations and chaos. Evolution can be twisted away from defection, toward cooperation. Adding "generous tit-for-tat" greatly increases the overall level of cooperation and can lead to long periods of steady cooperation. Since May's paper [May, R. M. (1976) Nature (London) 261, 459-467], "simple mathematical models with very complicated dynamics" have been found in many biological applications, but here we provide an example of a biologically relevant evolutionary game whose dynamics display deterministic chaos. The simulations bear some resemblance to the irregular cycles displayed by the frequencies of host genotypes and specialized parasites in evolutionary "arms races" [Hamilton, W. D., Axelrod, R. & Tanese, R. (1990) Proc. Natl. Acad. Sci. USA 87, 3566-3573; Seger, J. (1988) Philos. Trans. R. Soc. London B 319, 541-555].

Quantum games on evolving random networks

NASA Astrophysics Data System (ADS)

Pawela, Łukasz

2016-09-01

We study the advantages of quantum strategies in evolutionary social dilemmas on evolving random networks. We focus our study on the two-player games: prisoner's dilemma, snowdrift and stag-hunt games. The obtained result show the benefits of quantum strategies for the prisoner's dilemma game. For the other two games, we obtain regions of parameters where the quantum strategies dominate, as well as regions where the classical strategies coexist.

Cooperation for volunteering and partially random partnerships

NASA Astrophysics Data System (ADS)

Szabó, György; Vukov, Jeromos

2004-03-01

Competition among cooperative, defective, and loner strategies is studied by considering an evolutionary prisoner’s dilemma game for different partnerships. In this game each player can adopt one of its coplayer’s strategy with a probability depending on the difference of payoffs coming from games with the corresponding coplayers. Our attention is focused on the effects of annealed and quenched randomness in the partnership for fixed number of coplayers. It is shown that only the loners survive if the four coplayers are chosen randomly (mean-field limit). On the contrary, on the square lattice all the three strategies are maintained by the cyclic invasions resulting in a self-organizing spatial pattern. If the fixed partnership is described by a regular small-world structure then a homogeneous oscillation occurs in the population dynamics when the measure of quenched randomness exceeds a threshold value. Similar behavior with higher sensitivity to the randomness is found if temporary partners are substituted for the standard ones with some probability at each step of iteration.

Stochastic population dynamics in spatially extended predator-prey systems

NASA Astrophysics Data System (ADS)

Dobramysl, Ulrich; Mobilia, Mauro; Pleimling, Michel; Täuber, Uwe C.

2018-02-01

Spatially extended population dynamics models that incorporate demographic noise serve as case studies for the crucial role of fluctuations and correlations in biological systems. Numerical and analytic tools from non-equilibrium statistical physics capture the stochastic kinetics of these complex interacting many-particle systems beyond rate equation approximations. Including spatial structure and stochastic noise in models for predator-prey competition invalidates the neutral Lotka-Volterra population cycles. Stochastic models yield long-lived erratic oscillations stemming from a resonant amplification mechanism. Spatially extended predator-prey systems display noise-stabilized activity fronts that generate persistent correlations. Fluctuation-induced renormalizations of the oscillation parameters can be analyzed perturbatively via a Doi-Peliti field theory mapping of the master equation; related tools allow detailed characterization of extinction pathways. The critical steady-state and non-equilibrium relaxation dynamics at the predator extinction threshold are governed by the directed percolation universality class. Spatial predation rate variability results in more localized clusters, enhancing both competing species’ population densities. Affixing variable interaction rates to individual particles and allowing for trait inheritance subject to mutations induces fast evolutionary dynamics for the rate distributions. Stochastic spatial variants of three-species competition with ‘rock-paper-scissors’ interactions metaphorically describe cyclic dominance. These models illustrate intimate connections between population dynamics and evolutionary game theory, underscore the role of fluctuations to drive populations toward extinction, and demonstrate how space can support species diversity. Two-dimensional cyclic three-species May-Leonard models are characterized by the emergence of spiraling patterns whose properties are elucidated by a mapping onto a complex Ginzburg-Landau equation. Multiple-species extensions to general ‘food networks’ can be classified on the mean-field level, providing both fundamental understanding of ensuing cooperativity and profound insight into the rich spatio-temporal features and coarsening kinetics in the corresponding spatially extended systems. Novel space-time patterns emerge as a result of the formation of competing alliances; e.g. coarsening domains that each incorporate rock-paper-scissors competition games.

Evolutionary technology adoption in an oligopoly market with forward-looking firms

NASA Astrophysics Data System (ADS)

Lamantia, F.; Radi, D.

2018-05-01

In this paper, we propose an evolutionary oligopoly game of technology adoption in a market with isoelastic demand and two possible (linear) production technologies. While one technology is characterized by lower marginal costs, the magnitude of fixed costs entails that a technology does not necessarily dominate the other. Firms are forward-looking as they assess the profitability of employing either technology according to the corresponding expected profits. The dynamics of the system is studied through a piecewise-smooth map, for which we present a local stability analysis of equilibria and show the occurrence of smooth and border collision bifurcations. Global analysis of the model is also presented to show the coexistence of attractors and its economic significance. This investigation reveals that firms can fail to learn to adopt the more efficient technology.

Evolutionary technology adoption in an oligopoly market with forward-looking firms.

PubMed

Lamantia, F; Radi, D

2018-05-01

In this paper, we propose an evolutionary oligopoly game of technology adoption in a market with isoelastic demand and two possible (linear) production technologies. While one technology is characterized by lower marginal costs, the magnitude of fixed costs entails that a technology does not necessarily dominate the other. Firms are forward-looking as they assess the profitability of employing either technology according to the corresponding expected profits. The dynamics of the system is studied through a piecewise-smooth map, for which we present a local stability analysis of equilibria and show the occurrence of smooth and border collision bifurcations. Global analysis of the model is also presented to show the coexistence of attractors and its economic significance. This investigation reveals that firms can fail to learn to adopt the more efficient technology.

Truth and probability in evolutionary games

NASA Astrophysics Data System (ADS)

Barrett, Jeffrey A.

2017-01-01

This paper concerns two composite Lewis-Skyrms signalling games. Each consists in a base game that evolves a language descriptive of nature and a metagame that coevolves a language descriptive of the base game and its evolving language. The first composite game shows how a pragmatic notion of truth might coevolve with a simple descriptive language. The second shows how a pragmatic notion of probability might similarly coevolve. Each of these pragmatic notions is characterised by the particular game and role that it comes to play in the game.

Impact of heterogeneous activity and community structure on the evolutionary success of cooperators in social networks

NASA Astrophysics Data System (ADS)

Wu, Zhi-Xi; Rong, Zhihai; Yang, Han-Xin

2015-01-01

Recent empirical studies suggest that heavy-tailed distributions of human activities are universal in real social dynamics [L. Muchnik, S. Pei, L. C. Parra, S. D. S. Reis, J. S. Andrade Jr., S. Havlin, and H. A. Makse, Sci. Rep. 3, 1783 (2013), 10.1038/srep01783]. On the other hand, community structure is ubiquitous in biological and social networks [M. E. J. Newman, Nat. Phys. 8, 25 (2012), 10.1038/nphys2162]. Motivated by these facts, we here consider the evolutionary prisoner's dilemma game taking place on top of a real social network to investigate how the community structure and the heterogeneity in activity of individuals affect the evolution of cooperation. In particular, we account for a variation of the birth-death process (which can also be regarded as a proportional imitation rule from a social point of view) for the strategy updating under both weak and strong selection (meaning the payoffs harvested from games contribute either slightly or heavily to the individuals' performance). By implementing comparative studies, where the players are selected either randomly or in terms of their actual activities to play games with their immediate neighbors, we figure out that heterogeneous activity benefits the emergence of collective cooperation in a harsh environment (the action for cooperation is costly) under strong selection, whereas it impairs the formation of altruism under weak selection. Moreover, we find that the abundance of communities in the social network can evidently foster the formation of cooperation under strong selection, in contrast to the games evolving on randomized counterparts. Our results are therefore helpful for us to better understand the evolution of cooperation in real social systems.

The limits of weak selection and large population size in evolutionary game theory.

PubMed

Sample, Christine; Allen, Benjamin

2017-11-01

Evolutionary game theory is a mathematical approach to studying how social behaviors evolve. In many recent works, evolutionary competition between strategies is modeled as a stochastic process in a finite population. In this context, two limits are both mathematically convenient and biologically relevant: weak selection and large population size. These limits can be combined in different ways, leading to potentially different results. We consider two orderings: the [Formula: see text] limit, in which weak selection is applied before the large population limit, and the [Formula: see text] limit, in which the order is reversed. Formal mathematical definitions of the [Formula: see text] and [Formula: see text] limits are provided. Applying these definitions to the Moran process of evolutionary game theory, we obtain asymptotic expressions for fixation probability and conditions for success in these limits. We find that the asymptotic expressions for fixation probability, and the conditions for a strategy to be favored over a neutral mutation, are different in the [Formula: see text] and [Formula: see text] limits. However, the ordering of limits does not affect the conditions for one strategy to be favored over another.

Effects of directional migration on prisoner's dilemma game in a square domain

NASA Astrophysics Data System (ADS)

Cheng, Hongyan; Dai, Qionglin; Li, Haihong; Qian, Xiaolan; Zhang, Mei; Yang, Junzhong

2013-04-01

We introduce a new migration rule, the directional migration, into evolutionary prisoner's dilemma games defined in a square domain with periodic boundary conditions. We find that cooperation can be enhanced to a much higher level than the case in the absence of migration. Additionally, the presence of the directional migration has profound impact on the population structure: the directional migration drives individuals to form a number of dense clusters which resembles social cohesion. The evolutionary game theory incorporating the directional migration can reproduce some real characteristics of populations in human society and may shed light on the problem of social cohesion.

Recidivism and Rehabilitation of Criminal Offenders: A Carrot and Stick Evolutionary Game

PubMed Central

Berenji, Bijan; Chou, Tom; D'Orsogna, Maria R.

2014-01-01

Motivated by recent efforts by the criminal justice system to treat and rehabilitate nonviolent offenders rather than focusing solely on their punishment, we introduce an evolutionary game theoretic model to study the effects of “carrot and stick” intervention programs on criminal recidivism. We use stochastic simulations to study the evolution of a population where individuals may commit crimes depending on their past history, surrounding environment and, in the case of recidivists, on any counseling, educational or training programs available to them after being punished for their previous crimes. These sociological factors are embodied by effective parameters that determine the decision making probabilities. Players may decide to permanently reform or continue engaging in criminal activity, eventually reaching a state where they are considered incorrigible. Depending on parameter choices, the outcome of the game is a society with a majority of virtuous, rehabilitated citizens or incorrigibles. Since total resources may be limited, we constrain the combined punishment and rehabilitation costs per crime to be fixed, so that increasing one effort will necessarily decrease the other. We find that the most successful strategy in reducing crime is to optimally allocate resources so that after being punished, criminals experience impactful intervention programs, especially during the first stages of their return to society. Excessively harsh or lenient punishments are less effective. We also develop a system of coupled ordinary differential equations with memory effects to give a qualitative description of our simulated societal dynamics. We discuss our findings and sociological implications. PMID:24454884

Recidivism and rehabilitation of criminal offenders: a carrot and stick evolutionary game.

PubMed

Berenji, Bijan; Chou, Tom; D'Orsogna, Maria R

2014-01-01

Motivated by recent efforts by the criminal justice system to treat and rehabilitate nonviolent offenders rather than focusing solely on their punishment, we introduce an evolutionary game theoretic model to study the effects of "carrot and stick" intervention programs on criminal recidivism. We use stochastic simulations to study the evolution of a population where individuals may commit crimes depending on their past history, surrounding environment and, in the case of recidivists, on any counseling, educational or training programs available to them after being punished for their previous crimes. These sociological factors are embodied by effective parameters that determine the decision making probabilities. Players may decide to permanently reform or continue engaging in criminal activity, eventually reaching a state where they are considered incorrigible. Depending on parameter choices, the outcome of the game is a society with a majority of virtuous, rehabilitated citizens or incorrigibles. Since total resources may be limited, we constrain the combined punishment and rehabilitation costs per crime to be fixed, so that increasing one effort will necessarily decrease the other. We find that the most successful strategy in reducing crime is to optimally allocate resources so that after being punished, criminals experience impactful intervention programs, especially during the first stages of their return to society. Excessively harsh or lenient punishments are less effective. We also develop a system of coupled ordinary differential equations with memory effects to give a qualitative description of our simulated societal dynamics. We discuss our findings and sociological implications.

Phase transitions in adaptive competitive environments: Theories and applications of the minority game

NASA Astrophysics Data System (ADS)

Li, Yi

It is of great scientific significance to study the complex systems of agents with adaptive strategies competing for resources. In many of such systems in social and biological environments, agents succeed by making innovative choices. In this thesis, we model this behavior by presenting the results and analysis of a class of games in which heterogeneous agents are rewarded for being in a minority group. Each agent possesses a number of fixed strategies, each of which takes publicly available information as input to predict next group. Commonly known as the minority game, this simple model manifests a maladaptive, informationally efficient phase in which the system performs poorly at generating resources and an inefficient phase in which there is an emergent cooperation among the agents, and the system more effectively generates resources. The best emergent coordination is achieved at the phase transition, which occurs when z, the ratio of the dimension of the strategy space to the number of agents, is about 0.34. This model also has similar properties to a spin glass system thus statistical mechanics methods were employed to provide analytical results. The phase structure persists under variations such as variable payoff schemes and evolutionary mechanisms. Agents in real life are subject to local connectivity and incomplete information. A framework based on bi-graph was proposed to model these factors. In the context of economics, we proposed a stock market model incorporating delayed majority dynamics and agents holding heterogeneous expectations. We found that for a range of parameter settings, minority dynamics are dynamically induced, effectively reducing market volatility. Finally, we introduce a version of the minority game played by human participants. We observed emergent coordination of players' choices leading to increased average reward. Furthermore, players with the simplest strategies reap the most wealth.

Quantum decision-maker theory and simulation

NASA Astrophysics Data System (ADS)

Zak, Michail; Meyers, Ronald E.; Deacon, Keith S.

2000-07-01

A quantum device simulating the human decision making process is introduced. It consists of quantum recurrent nets generating stochastic processes which represent the motor dynamics, and of classical neural nets describing the evolution of probabilities of these processes which represent the mental dynamics. The autonomy of the decision making process is achieved by a feedback from the mental to motor dynamics which changes the stochastic matrix based upon the probability distribution. This feedback replaces unavailable external information by an internal knowledge- base stored in the mental model in the form of probability distributions. As a result, the coupled motor-mental dynamics is described by a nonlinear version of Markov chains which can decrease entropy without an external source of information. Applications to common sense based decisions as well as to evolutionary games are discussed. An example exhibiting self-organization is computed using quantum computer simulation. Force on force and mutual aircraft engagements using the quantum decision maker dynamics are considered.

Social genomics of healthy and disordered internet gaming.

PubMed

Snodgrass, Jeffrey G; Dengah Ii, H J François; Lacy, Michael G; Else, Robert J; Polzer, Evan R; Arevalo, Jesusa M G; Cole, Steven W

2018-06-20

To combine social genomics with cultural approaches to expand understandings of the somatic health dynamics of online gaming, including in the controversial nosological construct of internet gaming disorder (IGD). In blood samples from 56 U.S. gamers, we examined expression of the conserved transcriptional response to adversity (CTRA), a leukocyte gene expression profile activated by chronic stress. We compared positively engaged and problem gamers, as identified by an ethnographically developed measure, the Positive and Negative Gaming Experiences Scale (PNGE-42), and also by a clinically derived IGD scale (IGDS-SF9). CTRA profiles showed a clear relationship with PNGE-42, with a substantial linkage to offline social support, but were not meaningfully associated with disordered play as measured by IGDS-SF9. Our study advances understanding of the psychobiology of play, demonstrating via novel transcriptomic methods the association of negatively experienced internet play with biological measures of chronic threat, uncertainty, and distress. Our findings are consistent with the view that problematic patterns of online gaming are a proxy for broader patterns of biopsychosocial stress and distress such as loneliness, rather than a psychiatric disorder sui generis, which might exist apart from gamers' other life problems. By confirming the biological correlates of certain patterns of internet gaming, culturally-sensitive genomics approaches such as this can inform both evolutionary theorizing regarding the nature of play, as well as current psychiatric debates about the appropriateness of modeling distressful gaming on substance addiction and problem gambling. © 2018 Wiley Periodicals, Inc.

Peer pressure: enhancement of cooperation through mutual punishment.

PubMed

Yang, Han-Xin; Wu, Zhi-Xi; Rong, Zhihai; Lai, Ying-Cheng

2015-02-01

An open problem in evolutionary game dynamics is to understand the effect of peer pressure on cooperation in a quantitative manner. Peer pressure can be modeled by punishment, which has been proved to be an effective mechanism to sustain cooperation among selfish individuals. We investigate a symmetric punishment strategy, in which an individual will punish each neighbor if their strategies are different, and vice versa. Because of the symmetry in imposing the punishment, one might intuitively expect the strategy to have little effect on cooperation. Utilizing the prisoner's dilemma game as a prototypical model of interactions at the individual level, we find, through simulation and theoretical analysis, that proper punishment, when even symmetrically imposed on individuals, can enhance cooperation. Also, we find that the initial density of cooperators plays an important role in the evolution of cooperation driven by mutual punishment.

Peer pressure: Enhancement of cooperation through mutual punishment

NASA Astrophysics Data System (ADS)

Yang, Han-Xin; Wu, Zhi-Xi; Rong, Zhihai; Lai, Ying-Cheng

2015-02-01

An open problem in evolutionary game dynamics is to understand the effect of peer pressure on cooperation in a quantitative manner. Peer pressure can be modeled by punishment, which has been proved to be an effective mechanism to sustain cooperation among selfish individuals. We investigate a symmetric punishment strategy, in which an individual will punish each neighbor if their strategies are different, and vice versa. Because of the symmetry in imposing the punishment, one might intuitively expect the strategy to have little effect on cooperation. Utilizing the prisoner's dilemma game as a prototypical model of interactions at the individual level, we find, through simulation and theoretical analysis, that proper punishment, when even symmetrically imposed on individuals, can enhance cooperation. Also, we find that the initial density of cooperators plays an important role in the evolution of cooperation driven by mutual punishment.

Complex traffic flow that allows as well as hampers lane-changing intrinsically contains social-dilemma structures

NASA Astrophysics Data System (ADS)

Iwamura, Yoshiro; Tanimoto, Jun

2018-02-01

To investigate an interesting question as to whether or not social dilemma structures can be found in a realistic traffic flow reproduced by a model, we built a new microscopic model in which an intentional driver may try lane-changing to go in front of other vehicles and may hamper others’ lane-changes. Our model consists of twofold parts; cellular automaton emulating a real traffic flow and evolutionary game theory to implement a driver’s decision making-process. Numerical results reveal that a social dilemma like the multi-player chicken game or prisoner’s dilemma game emerges depending on the traffic phase. This finding implies that a social dilemma, which has been investigated by applied mathematics so far, hides behind a traffic flow, which has been explored by fluid dynamics. Highlight - Complex system of traffic flow with consideration of driver’s decision making process is concerned. - A new model dovetailing cellular automaton with game theory is established. - Statistical result from numerical simulations reveals a social dilemma structure underlying traffic flow. - The social dilemma is triggered by a driver’s egocentric actions of lane-changing and hampering other’s lane-change.

Evolutionary dynamics of populations with conflicting interactions: Classification and analytical treatment considering asymmetry and power

NASA Astrophysics Data System (ADS)

Helbing, Dirk; Johansson, Anders

2010-01-01

Evolutionary game theory has been successfully used to investigate the dynamics of systems, in which many entities have competitive interactions. From a physics point of view, it is interesting to study conditions under which a coordination or cooperation of interacting entities will occur, be it spins, particles, bacteria, animals, or humans. Here, we analyze the case, where the entities are heterogeneous, particularly the case of two populations with conflicting interactions and two possible states. For such systems, explicit mathematical formulas will be determined for the stationary solutions and the associated eigenvalues, which determine their stability. In this way, four different types of system dynamics can be classified and the various kinds of phase transitions between them will be discussed. While these results are interesting from a physics point of view, they are also relevant for social, economic, and biological systems, as they allow one to understand conditions for (1) the breakdown of cooperation, (2) the coexistence of different behaviors (“subcultures”), (3) the evolution of commonly shared behaviors (“norms”), and (4) the occurrence of polarization or conflict. We point out that norms have a similar function in social systems that forces have in physics.

CROSS-DISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY: Evolutionary Self-Questioning Games with Local Contribution

NASA Astrophysics Data System (ADS)

Liu, Yong-Kui; Li, Zhi; Chen, Xiao-Jie; Wang, Long

2009-08-01

We investigate the evolutionary Prisoner's Dilemma and the Snowdrift Game on small-world networks in a realistic social context where individuals consider their local contributions to their group and update their strategies by self-questioning. An individual with introspection can determine whether its current strategy is superior by playing a virtual round of the game and its local contribution is defined as the sum of all the payoffs its neighbors collect against it. In our model, the performance of an individual is determined by both its payoff and local contribution through a linear combination. We demonstrate that the present mechanism can produce very robust cooperative behavior in both games. Furthermore, we provide theoretical analysis based on mean-field approximation, and find that the analytical predictions are qualitatively consistent with the simulation results.

Cancer heterogeneity and multilayer spatial evolutionary games.

PubMed

Świerniak, Andrzej; Krześlak, Michał

2016-10-13

Evolutionary game theory (EGT) has been widely used to simulate tumour processes. In almost all studies on EGT models analysis is limited to two or three phenotypes. Our model contains four main phenotypes. Moreover, in a standard approach only heterogeneity of populations is studied, while cancer cells remain homogeneous. A multilayer approach proposed in this paper enables to study heterogeneity of single cells. In the extended model presented in this paper we consider four strategies (phenotypes) that can arise by mutations. We propose multilayer spatial evolutionary games (MSEG) played on multiple 2D lattices corresponding to the possible phenotypes. It enables simulation and investigation of heterogeneity on the player-level in addition to the population-level. Moreover, it allows to model interactions between arbitrary many phenotypes resulting from the mixture of basic traits. Different equilibrium points and scenarios (monomorphic and polymorphic populations) have been achieved depending on model parameters and the type of played game. However, there is a possibility of stable quadromorphic population in MSEG games for the same set of parameters like for the mean-field game. The model assumes an existence of four possible phenotypes (strategies) in the population of cells that make up tumour. Various parameters and relations between cells lead to complex analysis of this model and give diverse results. One of them is a possibility of stable coexistence of different tumour cells within the population, representing almost arbitrary mixture of the basic phenotypes. This article was reviewed by Tomasz Lipniacki, Urszula Ledzewicz and Jacek Banasiak.

Scheduling for the National Hockey League Using a Multi-objective Evolutionary Algorithm

NASA Astrophysics Data System (ADS)

Craig, Sam; While, Lyndon; Barone, Luigi

We describe a multi-objective evolutionary algorithm that derives schedules for the National Hockey League according to three objectives: minimising the teams' total travel, promoting equity in rest time between games, and minimising long streaks of home or away games. Experiments show that the system is able to derive schedules that beat the 2008-9 NHL schedule in all objectives simultaneously, and that it returns a set of schedules that offer a range of trade-offs across the objectives.

Stability and robustness analysis of cooperation cycles driven by destructive agents in finite populations

NASA Astrophysics Data System (ADS)

Requejo, Rubén J.; Camacho, Juan; Cuesta, José A.; Arenas, Alex

2012-08-01

The emergence and promotion of cooperation are two of the main issues in evolutionary game theory, as cooperation is amenable to exploitation by defectors, which take advantage of cooperative individuals at no cost, dooming them to extinction. It has been recently shown that the existence of purely destructive agents (termed jokers) acting on the common enterprises (public goods games) can induce stable limit cycles among cooperation, defection, and destruction when infinite populations are considered. These cycles allow for time lapses in which cooperators represent a relevant fraction of the population, providing a mechanism for the emergence of cooperative states in nature and human societies. Here we study analytically and through agent-based simulations the dynamics generated by jokers in finite populations for several selection rules. Cycles appear in all cases studied, thus showing that the joker dynamics generically yields a robust cyclic behavior not restricted to infinite populations. We also compute the average time in which the population consists mostly of just one strategy and compare the results with numerical simulations.

Sex differences in Nintendo Wii performance as expected from hunter-gatherer selection.

PubMed

Cherney, Isabelle D; Poss, Jordan L

2008-06-01

To test the hunter-gatherer theory of cognitive sex differences, men and women each played four video games on a Wii console: two games simulating skills necessary for hunting (navigation and shooting) and two games simulating skills necessary for gathering (fine motor and visual search). Men outperformed women on the two hunting games, whereas there were no sex differences on the gathering skill games. The findings are discussed in terms of evolutionary psychology theory.

Impact of deterministic and stochastic updates on network reciprocity in the prisoner's dilemma game

NASA Astrophysics Data System (ADS)

Tanimoto, Jun

2014-08-01

In 2 × 2 prisoner's dilemma games, network reciprocity is one mechanism for adding social viscosity, which leads to cooperative equilibrium. This study introduced an intriguing framework for the strategy update rule that allows any combination of a purely deterministic method, imitation max (IM), and a purely probabilistic one, pairwise Fermi (Fermi-PW). A series of simulations covering the whole range from IM to Fermi-PW reveals that, as a general tendency, the larger fractions of stochastic updating reduce network reciprocity, so long as the underlying lattice contains no noise in the degree of distribution. However, a small amount of stochastic flavor added to an otherwise perfectly deterministic update rule was actually found to enhance network reciprocity. This occurs because a subtle stochastic effect in the update rule improves the evolutionary trail in games having more stag-hunt-type dilemmas, although the same stochastic effect degenerates evolutionary trails in games having more chicken-type dilemmas. We explain these effects by dividing evolutionary trails into the enduring and expanding periods defined by Shigaki et al. [Phys. Rev. E 86, 031141 (2012), 10.1103/PhysRevE.86.031141].

Some results on ethnic conflicts based on evolutionary game simulation

NASA Astrophysics Data System (ADS)

Qin, Jun; Yi, Yunfei; Wu, Hongrun; Liu, Yuhang; Tong, Xiaonian; Zheng, Bojin

2014-07-01

The force of the ethnic separatism, essentially originating from the negative effect of ethnic identity, is damaging the stability and harmony of multiethnic countries. In order to eliminate the foundation of the ethnic separatism and set up a harmonious ethnic relationship, some scholars have proposed a viewpoint: ethnic harmony could be promoted by popularizing civic identity. However, this viewpoint is discussed only from a philosophical prospective and still lacks support of scientific evidences. Because ethnic group and ethnic identity are products of evolution and ethnic identity is the parochialism strategy under the perspective of game theory, this paper proposes an evolutionary game simulation model to study the relationship between civic identity and ethnic conflict based on evolutionary game theory. The simulation results indicate that: (1) the ratio of individuals with civic identity has a negative association with the frequency of ethnic conflicts; (2) ethnic conflict will not die out by killing all ethnic members once for all, and it also cannot be reduced by a forcible pressure, i.e., increasing the ratio of individuals with civic identity; (3) the average frequencies of conflicts can stay in a low level by promoting civic identity periodically and persistently.

Evolutionary games with self-questioning adaptive mechanism and the Ising model

NASA Astrophysics Data System (ADS)

Liu, J.; Xu, C.; Hui, P. M.

2017-09-01

A class of evolutionary games using a self-questioning strategy switching mechanism played in a population of connected agents is shown to behave as an Ising model Hamiltonian of spins connected in the same way. The payoff parameters combine to give the coupling between spins and an external magnetic field. The mapping covers the prisoner's dilemma, snowdrift and stag hunt games in structured populations. A well-mixed system is used to illustrate the equivalence. In a chain of agents/spins, the mapping to Ising model leads to an exact solution to the games effortlessly. The accuracy of standard approximations on the games can then be quantified. The site approximation is found to show varied accuracies depending on the payoff parameters, and the link approximation is shown to give the exact result in a chain but not in a closed form. The mapping established here connects two research areas, with each having much to offer to the other.

Evolutionary games on multilayer networks: a colloquium

NASA Astrophysics Data System (ADS)

Wang, Zhen; Wang, Lin; Szolnoki, Attila; Perc, Matjaž

2015-05-01

Networks form the backbone of many complex systems, ranging from the Internet to human societies. Accordingly, not only is the range of our interactions limited and thus best described and modeled by networks, it is also a fact that the networks that are an integral part of such models are often interdependent or even interconnected. Networks of networks or multilayer networks are therefore a more apt description of social systems. This colloquium is devoted to evolutionary games on multilayer networks, and in particular to the evolution of cooperation as one of the main pillars of modern human societies. We first give an overview of the most significant conceptual differences between single-layer and multilayer networks, and we provide basic definitions and a classification of the most commonly used terms. Subsequently, we review fascinating and counterintuitive evolutionary outcomes that emerge due to different types of interdependencies between otherwise independent populations. The focus is on coupling through the utilities of players, through the flow of information, as well as through the popularity of different strategies on different network layers. The colloquium highlights the importance of pattern formation and collective behavior for the promotion of cooperation under adverse conditions, as well as the synergies between network science and evolutionary game theory.

An evolutionary model of cooperation, fairness and altruistic punishment in public good games.

PubMed

Hetzer, Moritz; Sornette, Didier

2013-01-01

We identify and explain the mechanisms that account for the emergence of fairness preferences and altruistic punishment in voluntary contribution mechanisms by combining an evolutionary perspective together with an expected utility model. We aim at filling a gap between the literature on the theory of evolution applied to cooperation and punishment, and the empirical findings from experimental economics. The approach is motivated by previous findings on other-regarding behavior, the co-evolution of culture, genes and social norms, as well as bounded rationality. Our first result reveals the emergence of two distinct evolutionary regimes that force agents to converge either to a defection state or to a state of coordination, depending on the predominant set of self- or other-regarding preferences. Our second result indicates that subjects in laboratory experiments of public goods games with punishment coordinate and punish defectors as a result of an aversion against disadvantageous inequitable outcomes. Our third finding identifies disadvantageous inequity aversion as evolutionary dominant and stable in a heterogeneous population of agents endowed initially only with purely self-regarding preferences. We validate our model using previously obtained results from three independently conducted experiments of public goods games with punishment.

An Evolutionary Model of Cooperation, Fairness and Altruistic Punishment in Public Good Games

PubMed Central

Hetzer, Moritz; Sornette, Didier

2013-01-01

We identify and explain the mechanisms that account for the emergence of fairness preferences and altruistic punishment in voluntary contribution mechanisms by combining an evolutionary perspective together with an expected utility model. We aim at filling a gap between the literature on the theory of evolution applied to cooperation and punishment, and the empirical findings from experimental economics. The approach is motivated by previous findings on other-regarding behavior, the co-evolution of culture, genes and social norms, as well as bounded rationality. Our first result reveals the emergence of two distinct evolutionary regimes that force agents to converge either to a defection state or to a state of coordination, depending on the predominant set of self- or other-regarding preferences. Our second result indicates that subjects in laboratory experiments of public goods games with punishment coordinate and punish defectors as a result of an aversion against disadvantageous inequitable outcomes. Our third finding identifies disadvantageous inequity aversion as evolutionary dominant and stable in a heterogeneous population of agents endowed initially only with purely self-regarding preferences. We validate our model using previously obtained results from three independently conducted experiments of public goods games with punishment. PMID:24260101

Mutualism and evolutionary multiplayer games: revisiting the Red King.

PubMed

Gokhale, Chaitanya S; Traulsen, Arne

2012-11-22

Coevolution of two species is typically thought to favour the evolution of faster evolutionary rates helping a species keep ahead in the Red Queen race, where 'it takes all the running you can do to stay where you are'. In contrast, if species are in a mutualistic relationship, it was proposed that the Red King effect may act, where it can be beneficial to evolve slower than the mutualistic species. The Red King hypothesis proposes that the species which evolves slower can gain a larger share of the benefits. However, the interactions between the two species may involve multiple individuals. To analyse such a situation, we resort to evolutionary multiplayer games. Even in situations where evolving slower is beneficial in a two-player setting, faster evolution may be favoured in a multiplayer setting. The underlying features of multiplayer games can be crucial for the distribution of benefits. They also suggest a link between the evolution of the rate of evolution and group size.

An evolutionarily stable strategy and the critical point of hog futures trading entities based on replicator dynamic theory: 2006–2015 data for China’s 22 provinces

PubMed Central

Pang, Jinbo; Deng, Lingfei

2017-01-01

Although frequent fluctuations in domestic hog prices seriously affect the stability and robustness of the hog supply chain, hog futures (an effective hedging instrument) have not been listed in China. To better understand hog futures market hedging, it is important to study the steady state of intersubjective bidding. This paper uses evolutionary game theory to construct a game model between hedgers and speculators in the hog futures market, and replicator dynamic equations are then used to obtain the steady state between the two trading entities. The results show that the steady state is one in which hedgers adopt a “buy” strategy and speculators adopt a “do not speculate” strategy, but this type of extreme steady state is not easily realized. Thus, to explore the rational proportion of hedgers and speculators in the evolutionary stabilization strategy, bidding processes were simulated using weekly average hog prices from 2006 to 2015, such that the conditions under which hedgers and speculators achieve a steady state could be analyzed. This task was performed to achieve the stability critical point, and we show that only when the value of λ is satisfied and the conditions of hog futures price changes and futures price are satisfied can hedgers and speculators achieve a rational proportion and a stable hog futures market. This market can thus provide a valuable reference for the development of the Chinese hog futures market and the formulation and guidance of relevant departmental policies. PMID:28241024

An evolutionarily stable strategy and the critical point of hog futures trading entities based on replicator dynamic theory: 2006-2015 data for China's 22 provinces.

PubMed

Pang, Jinbo; Deng, Lingfei; Wang, Gangyi

2017-01-01

Although frequent fluctuations in domestic hog prices seriously affect the stability and robustness of the hog supply chain, hog futures (an effective hedging instrument) have not been listed in China. To better understand hog futures market hedging, it is important to study the steady state of intersubjective bidding. This paper uses evolutionary game theory to construct a game model between hedgers and speculators in the hog futures market, and replicator dynamic equations are then used to obtain the steady state between the two trading entities. The results show that the steady state is one in which hedgers adopt a "buy" strategy and speculators adopt a "do not speculate" strategy, but this type of extreme steady state is not easily realized. Thus, to explore the rational proportion of hedgers and speculators in the evolutionary stabilization strategy, bidding processes were simulated using weekly average hog prices from 2006 to 2015, such that the conditions under which hedgers and speculators achieve a steady state could be analyzed. This task was performed to achieve the stability critical point, and we show that only when the value of λ is satisfied and the conditions of hog futures price changes and futures price are satisfied can hedgers and speculators achieve a rational proportion and a stable hog futures market. This market can thus provide a valuable reference for the development of the Chinese hog futures market and the formulation and guidance of relevant departmental policies.

Evolutionary Game Analysis of Government Regulation and Enterprise Emission from the Perspective of Environmental Tax

NASA Astrophysics Data System (ADS)

Mai, Yazong

2017-12-01

In the context of the upcoming implementation of the environmental tax policy, there is a need for a focus on the relationship between government regulation and corporate emissions. To achieve the real effect of environmental tax policy, government need to regulate the illegal emissions of enterprises. Based on the hypothesis of bounded rationality, this paper analyses the strategic set of government regulators and polluting enterprises in the implementation of environmental tax policy. By using the evolutionary game model, the utility function and payoff matrix of the both sides are constructed, and the evolutionary analysis and strategy adjustment of the environmental governance target and the actual profit of the stakeholders are carried out. Thus, the wrong behaviours could be corrected so that the equilibrium of the evolutionary system can be achieved gradually, which could also get the evolutionary stable strategies of the government and the polluting enterprises in the implementation of environmental tax policy.

Applications and extensions of epigenetic game theory. Comment on: ;Epigenetic game theory: How to compute the epigenetic control of maternal-to-zygotic transition; by Qian Wang et al.

NASA Astrophysics Data System (ADS)

Wang, Yaqun

2017-03-01

The authors are to be congratulated for a thought-provoking article [1], which reviews the epigenetic game theory (epiGame) that utilizes differential equations to study the epigenetic control of embryo development. It is a novel application of evolutionary game theory and provides biology researchers with useful methodologies to address scientific questions related to biological coordination of competition and cooperation.

Cooperation in memory-based prisoner's dilemma game on interdependent networks

NASA Astrophysics Data System (ADS)

Luo, Chao; Zhang, Xiaolin; Liu, Hong; Shao, Rui

2016-05-01

Memory or so-called experience normally plays the important role to guide the human behaviors in real world, that is essential for rational decisions made by individuals. Hence, when the evolutionary behaviors of players with bounded rationality are investigated, it is reasonable to make an assumption that players in system are with limited memory. Besides, in order to unravel the intricate variability of complex systems in real world and make a highly integrative understanding of their dynamics, in recent years, interdependent networks as a comprehensive network structure have obtained more attention in this community. In this article, the evolution of cooperation in memory-based prisoner's dilemma game (PDG) on interdependent networks composed by two coupled square lattices is studied. Herein, all or part of players are endowed with finite memory ability, and we focus on the mutual influence of memory effect and interdependent network reciprocity on cooperation of spatial PDG. We show that the density of cooperation can be significantly promoted within an optimal region of memory length and interdependent strength. Furthermore, distinguished by whether having memory ability/external links or not, each kind of players on networks would have distinct evolutionary behaviors. Our work could be helpful to understand the emergence and maintenance of cooperation under the evolution of memory-based players on interdependent networks.

Competition of tolerant strategies in the spatial public goods game

NASA Astrophysics Data System (ADS)

Szolnoki, Attila; Perc, Matjaž

2016-08-01

Tolerance implies enduring trying circumstances with a fair and objective attitude. To determine whether evolutionary advantages might be stemming from diverse levels of tolerance in a population, we study a spatial public goods game, where in addition to cooperators, defectors, and loners, tolerant players are also present. Depending on the number of defectors within a group, a tolerant player can either cooperate in or abstain from a particular instance of the game. We show that the diversity of tolerance can give rise to synergistic effects, wherein players with a different threshold in terms of the tolerated number of defectors in a group compete most effectively against defection and default abstinence. Such synergistic associations can stabilise states of full cooperation where otherwise defection would dominate. We observe complex pattern formation that gives rise to an intricate phase diagram, where invisible yet stable strategy alliances require outmost care lest they are overlooked. Our results highlight the delicate importance of diversity and tolerance for the provisioning of public goods, and they reveal fascinating subtleties of the spatiotemporal dynamics that is due to the competition of subsystem solutions in structured populations.

Boosting cooperation by involving extortion in spatial prisoner's dilemma games

NASA Astrophysics Data System (ADS)

Wu, Zhi-Xi; Rong, Zhihai

2014-12-01

We study the evolution of cooperation in spatial prisoner's dilemma games with and without extortion by adopting the aspiration-driven strategy updating rule. We focus explicitly on how the strategy updating manner (whether synchronous or asynchronous) and also the introduction of extortion strategy affect the collective outcome of the games. By means of Monte Carlo simulations as well as dynamical cluster techniques, we find that the involvement of extortioners facilitates the boom of cooperators in the population (and whom can always dominate the population if the temptation to defect is not too large) for both synchronous and asynchronous strategy updating, in stark contrast to the other case, where cooperation is promoted for an intermediate aspiration level with synchronous strategy updating, but is remarkably inhibited if the strategy updating is implemented asynchronously. We explain the results by configurational analysis and find that the presence of extortion leads to the checkerboard-like ordering of cooperators and extortioners, which enable cooperators to prevail in the population with both strategy updating manners. Moreover, extortion itself is evolutionary stable, and therefore acts as the incubator for the evolution of cooperation.

Punishment in the form of shared cost promotes altruism in the cooperative dilemma games.

PubMed

Zhang, Chunyan; Zhu, Yuying; Chen, Zengqiang; Zhang, Jianlei

2017-05-07

One phenomenon or social institution often observed in multi-agent interactions is the altruistic punishment, i.e. the punishment of unfair behavior by others at a personal cost. Inspired by the works focusing on punishment and the intricate mechanism behind it, we theoretically study the strategy evolution in the framework of two-strategy game models with the punishment on defectors, moreover, the cost of punishing will be evenly shared among the cooperators. Theoretical computations suggest that larger punishment on defectors or smaller punishment cost incurred by cooperators will enhance the fixation of altruistic cooperation in the population. Through the replicate dynamics, the group size of the randomly selected individuals from the sufficiently large population will notably affect the strategy evolution in populations nested within a dilemma. By theoretical modeling the concept of shared cost for punishment from one point of view, our findings underscore the importance of punishment with shared cost as a factor in real-life decisions in an evolutionary game context. Copyright © 2017 Elsevier Ltd. All rights reserved.

Why interdisciplinary research enriches the study of crime. Comment on "Statistical physics of crime: A review" by M.R. D'Orsogna and M. Perc

NASA Astrophysics Data System (ADS)

Donnay, Karsten

2015-03-01

The past several years have seen a rapidly growing interest in the use of advanced quantitative methodologies and formalisms adapted from the natural sciences to study a broad range of social phenomena. The research field of computational social science [1,2], for example, uses digital artifacts of human online activity to cast a new light on social dynamics. Similarly, the studies reviewed by D'Orsogna and Perc showcase a diverse set of advanced quantitative techniques to study the dynamics of crime. Methods used range from partial differential equations and self-exciting point processes to agent-based models, evolutionary game theory and network science [3].

Human Evolution, Movement, and Intelligence: Why Playing Games Counts as Smart

ERIC Educational Resources Information Center

Kretchmar, R. Scott

2018-01-01

The article investigates several ways in which creating, entering, and playing games requires uniquely human levels of intelligence. It examines an element of our evolutionary heritage and the possibility that games (particularly in the form of sport) were among the first elements of culture. It describes sport as a "way of knowing," a…

Evolutionary game theory for physical and biological scientists. II. Population dynamics equations can be associated with interpretations

PubMed Central

Liao, David; Tlsty, Thea D.

2014-01-01

The use of mathematical equations to analyse population dynamics measurements is being increasingly applied to elucidate complex dynamic processes in biological systems, including cancer. Purely ‘empirical’ equations may provide sufficient accuracy to support predictions and therapy design. Nevertheless, interpretation of fitting equations in terms of physical and biological propositions can provide additional insights that can be used both to refine models that prove inconsistent with data and to understand the scope of applicability of models that validate. The purpose of this tutorial is to assist readers in mathematically associating interpretations with equations and to provide guidance in choosing interpretations and experimental systems to investigate based on currently available biological knowledge, techniques in mathematical and computational analysis and methods for in vitro and in vivo experiments. PMID:25097752

INTERDISCIPLINARY PHYSICS AND RELATED AREAS OF SCIENCE AND TECHNOLOGY: Coexistence and Extinction Pattern of Asymmetric Cyclic Game Species in a Square Lattice

NASA Astrophysics Data System (ADS)

Dong, Lin-Rong; Li, Yong-Ming; Yang, Guang-Can

2010-06-01

The co-evolutionary dynamics of a cyclic game system is investigated in a two-dimensional square lattice with the asymmetrical rates for three species. Different with the well-mixed system, coexistence and extinction emerge alternately in the system, where a “zero-one" behavior is robust for a small population size, whereas, the system is predominated by coexistence for a big population one. We study in detail the influence about the fluctuation to the change of the state, and find that the difference between the maximal amplitude about the fluctuation and the average intensity determines which state the system is ultimately. In addition, we introduce Potts energy to explain the reason of the “zero-one" behavior. It is shown that the average Potts energy per site is the distance to the “zero-one" behavior in the model.

Beyond pairwise strategy updating in the prisoner's dilemma game

NASA Astrophysics Data System (ADS)

Wang, Xiaofeng; Perc, Matjaž; Liu, Yongkui; Chen, Xiaojie; Wang, Long

2012-10-01

In spatial games players typically alter their strategy by imitating the most successful or one randomly selected neighbor. Since a single neighbor is taken as reference, the information stemming from other neighbors is neglected, which begets the consideration of alternative, possibly more realistic approaches. Here we show that strategy changes inspired not only by the performance of individual neighbors but rather by entire neighborhoods introduce a qualitatively different evolutionary dynamics that is able to support the stable existence of very small cooperative clusters. This leads to phase diagrams that differ significantly from those obtained by means of pairwise strategy updating. In particular, the survivability of cooperators is possible even by high temptations to defect and over a much wider uncertainty range. We support the simulation results by means of pair approximations and analysis of spatial patterns, which jointly highlight the importance of local information for the resolution of social dilemmas.

A resource-based game theoretical approach for the paradox of the plankton.

PubMed

Huang, Weini; de Araujo Campos, Paulo Roberto; Moraes de Oliveira, Viviane; Fagundes Ferrreira, Fernando

2016-01-01

The maintenance of species diversity is a central focus in ecology. It is not rare to observe more species than the number of limiting resources, especially in plankton communities. However, such high species diversity is hard to achieve in theory under the competitive exclusion principles, known as the plankton paradox. Previous studies often focus on the coexistence of predefined species and ignore the fact that species can evolve. We model multi-resource competitions using evolutionary games, where the number of species fluctuates under extinction and the appearance of new species. The interspecific and intraspecific competitions are captured by a dynamical payoff matrix, which has a size of the number of species. The competition strength (payoff entries) is obtained from comparing the capability of species in consuming resources, which can change over time. This allows for the robust coexistence of a large number of species, providing a possible solution to the plankton paradox.

A resource-based game theoretical approach for the paradox of the plankton

PubMed Central

de Araujo Campos, Paulo Roberto; Moraes de Oliveira, Viviane

2016-01-01

The maintenance of species diversity is a central focus in ecology. It is not rare to observe more species than the number of limiting resources, especially in plankton communities. However, such high species diversity is hard to achieve in theory under the competitive exclusion principles, known as the plankton paradox. Previous studies often focus on the coexistence of predefined species and ignore the fact that species can evolve. We model multi-resource competitions using evolutionary games, where the number of species fluctuates under extinction and the appearance of new species. The interspecific and intraspecific competitions are captured by a dynamical payoff matrix, which has a size of the number of species. The competition strength (payoff entries) is obtained from comparing the capability of species in consuming resources, which can change over time. This allows for the robust coexistence of a large number of species, providing a possible solution to the plankton paradox. PMID:27602293

Epigenetic information in gametes: Gaming from before fertilization. Comment on ;Epigenetic game theory: How to compute the epigenetic control of maternal-to-zygotic transition; by Qian Wang et al.

NASA Astrophysics Data System (ADS)

Shi, Junchao; Zhang, Xudong; Liu, Ying; Chen, Qi

2017-03-01

In their interesting article [1] Wang et al. proposed a mathematical model based on evolutionary game theory [2] to tackle the fundamental question in embryo development, that how sperm and egg interact with each other, through epigenetic processes, to form a zygote and direct successful embryo development. This work is based on the premise that epigenetic reprogramming (referring to the erasure and reconstruction of epigenetic marks, such as DNA methylation and histone modifications) after fertilization might be of paramount importance to maintain the normal development of embryos, a premise we fully agree, given the compelling experimental evidence reported [3]. Wang et al. have specifically chosen to employ the well-studied DNA methylation reprogramming process during mammalian early embryo development, as a basis to develop their mathematical model, namely epigenetic game theory (epiGame). They concluded that the DNA methylation pattern in mammalian early embryo could be formulated and quantified, and their model can be further used to quantify the interactions, such as competition and/or cooperation of expressed genes that maximize the fitness of embryos. The efforts by Wang et al. in quantitatively and systematically analyzing the beginning of life apparently hold value and represent a novel direction for future embryo development research from both theoretical and experimental biologists. On the other hand, we see their theory still at its infancy, because there are plenty more parameters to consider and there are spaces for debates, such as the cases of haploid embryo development [4]. Here, we briefly comment on the dynamic process of epigenetic reprogramming that goes beyond DNA methylation, a dynamic interplay that involves histone modifications, non-coding RNAs, transposable elements et al., as well as the potential input of the various types of 'hereditary' epigenetic information in the gametes - a game that has started before the fertilization.

Evolutionary games and spatial chaos

NASA Astrophysics Data System (ADS)

Nowak, Martin A.; May, Robert M.

1992-10-01

MUCH attention has been given to the Prisoners' Dilemma as a metaphor for the problems surrounding the evolution of coopera-tive behaviour1-6. This work has dealt with the relative merits of various strategies (such as tit-for-tat) when players who recognize each other meet repeatedly, and more recently with ensembles of strategies and with the effects of occasional errors. Here we neglect all strategical niceties or memories of past encounters, considering only two simple kinds of players: those who always cooperate and those who always defect. We explore the consequences of placing these players in a two-dimensional spatial array: in each round, every individual 'plays the game' with the immediate neighbours; after this, each site is occupied either by its original owner or by one of the neighbours, depending on who scores the highest total in that round; and so to the next round of the game. This simple, and purely deterministic, spatial version of the Prisoners' Dilemma, with no memories among players and no strategical elaboration, can generate chaotically changing spatial patterns, in which cooperators and defectors both persist indefinitely (in fluctuating proportions about predictable long-term averages). If the starting configurations are sufficiently symmetrical, these ever-changing sequences of spatial patterns-dynamic fractals-can be extraordinarily beautiful, and have interesting mathematical properties. There are potential implications for the dynamics of a wide variety of spatially extended systems in physics and biology.

Effects of strategy-migration direction and noise in the evolutionary spatial prisoner's dilemma

NASA Astrophysics Data System (ADS)

Wu, Zhi-Xi; Holme, Petter

2009-08-01

Spatial games are crucial for understanding patterns of cooperation in nature (and to some extent society). They are known to be more sensitive to local symmetries than, e.g., spin models. This paper concerns the evolution of the prisoner’s dilemma game on regular lattices with three different types of neighborhoods—the von Neumann, Moore, and kagomé types. We investigate two kinds of dynamics for the players to update their strategies (that can be unconditional cooperator or defector). Depending on the payoff difference, an individual can adopt the strategy of a random neighbor [a voter-model-like dynamics (VMLD)] or impose its strategy on a random neighbor, i.e., invasion-process-like dynamics (IPLD). In particular, we focus on the effects of noise, in combination with the strategy dynamics, on the evolution of cooperation. We find that VMLD, compared to IPLD, better supports the spreading and sustaining of cooperation. We see that noise has nontrivial effects on the evolution of cooperation: maximum cooperation density can be realized either at a medium noise level, in the limit of zero noise or in both these regions. The temptation to defect and the local interaction structure determine the outcome. Especially, in the low noise limit, the local interaction plays a crucial role in determining the fate of cooperators. We elucidate these both by numerical simulations and mean-field cluster approximation methods.

Punishment does not promote cooperation under exploration dynamics when anti-social punishment is possible.

PubMed

P Hauser, Oliver; A Nowak, Martin; G Rand, David

2014-11-07

It has been argued that punishment promotes the evolution of cooperation when mutation rates are high (i.e. when agents engage in 'exploration dynamics'). Mutations maintain a steady supply of agents that punish free-riders, and thus free-riders are at a disadvantage. Recent experiments, however, have demonstrated that free-riders sometimes also pay to punish cooperators. Inspired by these empirical results, theoretical work has explored evolutionary dynamics where mutants are rare, and found that punishment does not promote the evolution of cooperation when this 'anti-social punishment' is allowed. Here we extend previous theory by studying the effect of anti-social punishment on the evolution of cooperation across higher mutation rates, and by studying voluntary as well as compulsory Public Goods Games. We find that for intermediate and high mutation rates, adding punishment does not promote cooperation in either compulsory or voluntary public goods games if anti-social punishment is possible. This is because mutations generate agents that punish cooperators just as frequently as agents that punish defectors, and these two effects cancel each other out. These results raise questions about the effectiveness of punishment for promoting cooperation when mutations are common, and highlight how decisions about which strategies to include in the strategy set can have profound effects on the resulting dynamics. Copyright © 2014 Elsevier Ltd. All rights reserved.

Evolutionary dynamics of fluctuating populations with strong mutualism

NASA Astrophysics Data System (ADS)

Chotibut, Thiparat; Nelson, David

2013-03-01

Evolutionary game theory with finite interacting populations is receiving increased attention, including subtle phenomena associated with number fluctuations, i.e., ``genetic drift.'' Models of cooperation and competition often utilize a simplified Moran model, with a strictly fixed total population size. We explore a more general evolutionary model with independent fluctuations in the numbers of two distinct species, in a regime characterized by ``strong mutualism.'' The model has two absorbing states, each corresponding to fixation of one of the two species, and allows exploration of the interplay between growth, competition, and mutualism. When mutualism is favored, number fluctuations eventually drive the system away from a stable fixed point, characterized by cooperation, to one of the absorbing states. Well-mixed populations will thus be taken over by a single species in a finite time, despite the bias towards cooperation. We calculate both the fixation probability and the mean fixation time as a function of the initial conditions and carrying capacities in the strong mutualism regime, using the method of matched asymptotic expansions. Our results are compared to computer simulations.

Evolutionary Dynamics of Nitrogen Fixation in the Legume–Rhizobia Symbiosis

PubMed Central

Fujita, Hironori; Aoki, Seishiro; Kawaguchi, Masayoshi

2014-01-01

The stabilization of host–symbiont mutualism against the emergence of parasitic individuals is pivotal to the evolution of cooperation. One of the most famous symbioses occurs between legumes and their colonizing rhizobia, in which rhizobia extract nutrients (or benefits) from legume plants while supplying them with nitrogen resources produced by nitrogen fixation (or costs). Natural environments, however, are widely populated by ineffective rhizobia that extract benefits without paying costs and thus proliferate more efficiently than nitrogen-fixing cooperators. How and why this mutualism becomes stabilized and evolutionarily persists has been extensively discussed. To better understand the evolutionary dynamics of this symbiosis system, we construct a simple model based on the continuous snowdrift game with multiple interacting players. We investigate the model using adaptive dynamics and numerical simulations. We find that symbiotic evolution depends on the cost–benefit balance, and that cheaters widely emerge when the cost and benefit are similar in strength. In this scenario, the persistence of the symbiotic system is compatible with the presence of cheaters. This result suggests that the symbiotic relationship is robust to the emergence of cheaters, and may explain the prevalence of cheating rhizobia in nature. In addition, various stabilizing mechanisms, such as partner fidelity feedback, partner choice, and host sanction, can reinforce the symbiotic relationship by affecting the fitness of symbionts in various ways. This result suggests that the symbiotic relationship is cooperatively stabilized by various mechanisms. In addition, mixed nodule populations are thought to encourage cheater emergence, but our model predicts that, in certain situations, cheaters can disappear from such populations. These findings provide a theoretical basis of the evolutionary dynamics of legume–rhizobia symbioses, which is extendable to other single-host, multiple-colonizer systems. PMID:24691447

Objects of consciousness

PubMed Central

Hoffman, Donald D.; Prakash, Chetan

2014-01-01

Current models of visual perception typically assume that human vision estimates true properties of physical objects, properties that exist even if unperceived. However, recent studies of perceptual evolution, using evolutionary games and genetic algorithms, reveal that natural selection often drives true perceptions to extinction when they compete with perceptions tuned to fitness rather than truth: Perception guides adaptive behavior; it does not estimate a preexisting physical truth. Moreover, shifting from evolutionary biology to quantum physics, there is reason to disbelieve in preexisting physical truths: Certain interpretations of quantum theory deny that dynamical properties of physical objects have definite values when unobserved. In some of these interpretations the observer is fundamental, and wave functions are compendia of subjective probabilities, not preexisting elements of physical reality. These two considerations, from evolutionary biology and quantum physics, suggest that current models of object perception require fundamental reformulation. Here we begin such a reformulation, starting with a formal model of consciousness that we call a “conscious agent.” We develop the dynamics of interacting conscious agents, and study how the perception of objects and space-time can emerge from such dynamics. We show that one particular object, the quantum free particle, has a wave function that is identical in form to the harmonic functions that characterize the asymptotic dynamics of conscious agents; particles are vibrations not of strings but of interacting conscious agents. This allows us to reinterpret physical properties such as position, momentum, and energy as properties of interacting conscious agents, rather than as preexisting physical truths. We sketch how this approach might extend to the perception of relativistic quantum objects, and to classical objects of macroscopic scale. PMID:24987382

Cancer treatment as a game: integrating evolutionary game theory into the optimal control of chemotherapy

NASA Astrophysics Data System (ADS)

Orlando, Paul A.; Gatenby, Robert A.; Brown, Joel S.

2012-12-01

Chemotherapy for metastatic cancer commonly fails due to evolution of drug resistance in tumor cells. Here, we view cancer treatment as a game in which the oncologists choose a therapy and tumors ‘choose’ an adaptive strategy. We propose the oncologist can gain an upper hand in the game by choosing treatment strategies that anticipate the adaptations of the tumor. In particular, we examine the potential benefit of exploiting evolutionary tradeoffs in tumor adaptations to therapy. We analyze a math model where cancer cells face tradeoffs in allocation of resistance to two drugs. The tumor ‘chooses’ its strategy by natural selection and the oncologist chooses her strategy by solving a control problem. We find that when tumor cells perform best by investing resources to maximize response to one drug the optimal therapy is a time-invariant delivery of both drugs simultaneously. However, if cancer cells perform better using a generalist strategy allowing resistance to both drugs simultaneously, then the optimal protocol is a time varying solution in which the two drug concentrations negatively covary. However, drug interactions can significantly alter these results. We conclude that knowledge of both evolutionary tradeoffs and drug interactions is crucial in planning optimal chemotherapy schedules for individual patients.

Economic principles in communication: an experimental study.

PubMed

De Jaegher, Kris; Rosenkranz, Stephanie; Weitzel, Utz

2014-12-21

This paper experimentally investigates how economic principles affect communication. In a simple sender-receiver game with common interests over payoffs, the sender can send a signal without a pre-given meaning in an infrequent or frequent state of the world. When the signal is costly, several theories (focal point theory, the intuitive criterion, evolutionary game theory) predict an efficient separating equilibrium, where the signal is sent in the infrequent state of the world (also referred to as Horn׳s rule). To analyze whether Horn׳s rule applies, and if so, which theory best explains it, we develop and test variants of the sender-receiver game where the theories generate discriminatory hypotheses. In costly signaling variants, our participants follow Horn׳s rule most of the time, in a manner that is best explained by focal point theory. In costless signaling variants, evolutionary game theory best explains our results. Here participants coordinate significantly more (less) often on a separating equilibrium where the signal is sent in the frequent state if they are primed to associate the absence of a signal with the infrequent (frequent) state of the world. We also find indications that a similar priming effect applies to costly signals. Thus, while the frequency with which participants follow Horn׳s rule in costly signaling variants is best explained by Horn׳s rule, the priming effect shows that some of our participants׳ behavior is best explained by evolutionary game theory even when signals are costly. Copyright © 2014 Elsevier Ltd. All rights reserved.

How can we model selectively neutral density dependence in evolutionary games.

PubMed

Argasinski, Krzysztof; Kozłowski, Jan

2008-03-01

The problem of density dependence appears in all approaches to the modelling of population dynamics. It is pertinent to classic models (i.e., Lotka-Volterra's), and also population genetics and game theoretical models related to the replicator dynamics. There is no density dependence in the classic formulation of replicator dynamics, which means that population size may grow to infinity. Therefore the question arises: How is unlimited population growth suppressed in frequency-dependent models? Two categories of solutions can be found in the literature. In the first, replicator dynamics is independent of background fitness. In the second type of solution, a multiplicative suppression coefficient is used, as in a logistic equation. Both approaches have disadvantages. The first one is incompatible with the methods of life history theory and basic probabilistic intuitions. The logistic type of suppression of per capita growth rate stops trajectories of selection when population size reaches the maximal value (carrying capacity); hence this method does not satisfy selective neutrality. To overcome these difficulties, we must explicitly consider turn-over of individuals dependent on mortality rate. This new approach leads to two interesting predictions. First, the equilibrium value of population size is lower than carrying capacity and depends on the mortality rate. Second, although the phase portrait of selection trajectories is the same as in density-independent replicator dynamics, pace of selection slows down when population size approaches equilibrium, and then remains constant and dependent on the rate of turn-over of individuals.

Coevolving agent strategies and network topology for the public goods games

NASA Astrophysics Data System (ADS)

Zhang, C. Y.; Zhang, J. L.; Xie, G. M.; Wang, L.

2011-03-01

Much of human cooperation remains an evolutionary riddle. Coevolutionary public goods games in structured populations are studied where players can change from an unproductive public goods game to a productive one, by evaluating the productivity of the public goods games. In our model, each individual participates in games organized by its neighborhood plus by itself. Coevolution here refers to an evolutionary process entailing both deletion of existing links and addition of new links between agents that accompanies the evolution of their strategies. Furthermore, we investigate the effects of time scale separation of strategy and structure on cooperation level. This study presents the following: Foremost, we observe that high cooperation levels in public goods interactions are attained by the entangled coevolution of strategy and structure. Presented results also confirm that the resulting networks show many features of real systems, such as cooperative behavior and hierarchical clustering. The heterogeneity of the interaction network is held responsible for the observed promotion of cooperation. We hope our work may offer an explanation for the origin of large-scale cooperative behavior among unrelated individuals.

Cooperation and punishment in an adversarial game: How defectors pave the way to a peaceful society

NASA Astrophysics Data System (ADS)

Short, M. B.; Brantingham, P. J.; D'Orsogna, M. R.

2010-12-01

The evolution of human cooperation has been the subject of much research, especially within the framework of evolutionary public goods games, where several mechanisms have been proposed to account for persistent cooperation. Yet, in addressing this issue, little attention has been given to games of a more adversarial nature, in which defecting players, rather than simply free riding, actively seek to harm others. Here, we develop an adversarial evolutionary game using the specific example of criminal activity, recasting the familiar public goods strategies of punishers, cooperators, and defectors in this light. We then introduce a strategy—the informant—with no clear analog in public goods games and show that individuals employing this strategy are a key to the emergence of systems where cooperation dominates. We also find that a defection-dominated regime may be transitioned to one that is cooperation-dominated by converting an optimal number of players into informants. We discuss these findings, the role of informants, and possible intervention strategies in extreme adversarial societies, such as those marred by wars and insurgencies.

Joint attention and language evolution

NASA Astrophysics Data System (ADS)

Kwisthout, Johan; Vogt, Paul; Haselager, Pim; Dijkstra, Ton

2008-06-01

This study investigates how more advanced joint attentional mechanisms, rather than only shared attention between two agents and an object, can be implemented and how they influence the results of language games played by these agents. We present computer simulations with language games showing that adding constructs that mimic the three stages of joint attention identified in children's early development (checking attention, following attention, and directing attention) substantially increase the performance of agents in these language games. In particular, the rates of improved performance for the individual attentional mechanisms have the same ordering as that of the emergence of these mechanisms in infants' development. These results suggest that language evolution and joint attentional mechanisms have developed in a co-evolutionary way, and that the evolutionary emergence of the individual attentional mechanisms is ordered just like their developmental emergence.

Dynamic game balancing implementation using adaptive algorithm in mobile-based Safari Indonesia game

NASA Astrophysics Data System (ADS)

Yuniarti, Anny; Nata Wardanie, Novita; Kuswardayan, Imam

2018-03-01

In developing a game there is one method that should be applied to maintain the interest of players, namely dynamic game balancing. Dynamic game balancing is a process to match a player’s playing style with the behaviour, attributes, and game environment. This study applies dynamic game balancing using adaptive algorithm in scrolling shooter game type called Safari Indonesia which developed using Unity. The game of this type is portrayed by a fighter aircraft character trying to defend itself from insistent enemy attacks. This classic game is chosen to implement adaptive algorithms because it has quite complex attributes to be developed using dynamic game balancing. Tests conducted by distributing questionnaires to a number of players indicate that this method managed to reduce frustration and increase the pleasure factor in playing.

Evolutionary robotics simulations help explain why reciprocity is rare in nature

PubMed Central

André, Jean-Baptiste; Nolfi, Stefano

2016-01-01

The relative rarity of reciprocity in nature, contrary to theoretical predictions that it should be widespread, is currently one of the major puzzles in social evolution theory. Here we use evolutionary robotics to solve this puzzle. We show that models based on game theory are misleading because they neglect the mechanics of behavior. In a series of experiments with simulated robots controlled by artificial neural networks, we find that reciprocity does not evolve, and show that this results from a general constraint that likely also prevents it from evolving in the wild. Reciprocity can evolve if it requires very few mutations, as is usually assumed in evolutionary game theoretic models, but not if, more realistically, it requires the accumulation of many adaptive mutations. PMID:27616139

Using Nonlinear Stochastic Evolutionary Game Strategy to Model an Evolutionary Biological Network of Organ Carcinogenesis Under a Natural Selection Scheme

PubMed Central

Chen, Bor-Sen; Tsai, Kun-Wei; Li, Cheng-Wei

2015-01-01

Molecular biologists have long recognized carcinogenesis as an evolutionary process that involves natural selection. Cancer is driven by the somatic evolution of cell lineages. In this study, the evolution of somatic cancer cell lineages during carcinogenesis was modeled as an equilibrium point (ie, phenotype of attractor) shifting, the process of a nonlinear stochastic evolutionary biological network. This process is subject to intrinsic random fluctuations because of somatic genetic and epigenetic variations, as well as extrinsic disturbances because of carcinogens and stressors. In order to maintain the normal function (ie, phenotype) of an evolutionary biological network subjected to random intrinsic fluctuations and extrinsic disturbances, a network robustness scheme that incorporates natural selection needs to be developed. This can be accomplished by selecting certain genetic and epigenetic variations to modify the network structure to attenuate intrinsic fluctuations efficiently and to resist extrinsic disturbances in order to maintain the phenotype of the evolutionary biological network at an equilibrium point (attractor). However, during carcinogenesis, the remaining (or neutral) genetic and epigenetic variations accumulate, and the extrinsic disturbances become too large to maintain the normal phenotype at the desired equilibrium point for the nonlinear evolutionary biological network. Thus, the network is shifted to a cancer phenotype at a new equilibrium point that begins a new evolutionary process. In this study, the natural selection scheme of an evolutionary biological network of carcinogenesis was derived from a robust negative feedback scheme based on the nonlinear stochastic Nash game strategy. The evolvability and phenotypic robustness criteria of the evolutionary cancer network were also estimated by solving a Hamilton–Jacobi inequality – constrained optimization problem. The simulation revealed that the phenotypic shift of the lung cancer-associated cell network takes 54.5 years from a normal state to stage I cancer, 1.5 years from stage I to stage II cancer, and 2.5 years from stage II to stage III cancer, with a reasonable match for the statistical result of the average age of lung cancer. These results suggest that a robust negative feedback scheme, based on a stochastic evolutionary game strategy, plays a critical role in an evolutionary biological network of carcinogenesis under a natural selection scheme. PMID:26244004

Climbing Mount Probable

ERIC Educational Resources Information Center

Harper, Marc Allen

2009-01-01

This work attempts to explain the relationships between natural selection, information theory, and statistical inference. In particular, a geometric formulation of information theory known as information geometry and its deep connections to evolutionary game theory inform the role of natural selection in evolutionary processes. The goals of this…

Evolutionary Establishment of Moral and Double Moral Standards through Spatial Interactions

PubMed Central

Helbing, Dirk; Szolnoki, Attila; Perc, Matjaž; Szabó, György

2010-01-01

Situations where individuals have to contribute to joint efforts or share scarce resources are ubiquitous. Yet, without proper mechanisms to ensure cooperation, the evolutionary pressure to maximize individual success tends to create a tragedy of the commons (such as over-fishing or the destruction of our environment). This contribution addresses a number of related puzzles of human behavior with an evolutionary game theoretical approach as it has been successfully used to explain the behavior of other biological species many times, from bacteria to vertebrates. Our agent-based model distinguishes individuals applying four different behavioral strategies: non-cooperative individuals (“defectors”), cooperative individuals abstaining from punishment efforts (called “cooperators” or “second-order free-riders”), cooperators who punish non-cooperative behavior (“moralists”), and defectors, who punish other defectors despite being non-cooperative themselves (“immoralists”). By considering spatial interactions with neighboring individuals, our model reveals several interesting effects: First, moralists can fully eliminate cooperators. This spreading of punishing behavior requires a segregation of behavioral strategies and solves the “second-order free-rider problem”. Second, the system behavior changes its character significantly even after very long times (“who laughs last laughs best effect”). Third, the presence of a number of defectors can largely accelerate the victory of moralists over non-punishing cooperators. Fourth, in order to succeed, moralists may profit from immoralists in a way that appears like an “unholy collaboration”. Our findings suggest that the consideration of punishment strategies allows one to understand the establishment and spreading of “moral behavior” by means of game-theoretical concepts. This demonstrates that quantitative biological modeling approaches are powerful even in domains that have been addressed with non-mathematical concepts so far. The complex dynamics of certain social behaviors become understandable as the result of an evolutionary competition between different behavioral strategies. PMID:20454464

When the mean is not enough: Calculating fixation time distributions in birth-death processes.

PubMed

Ashcroft, Peter; Traulsen, Arne; Galla, Tobias

2015-10-01

Studies of fixation dynamics in Markov processes predominantly focus on the mean time to absorption. This may be inadequate if the distribution is broad and skewed. We compute the distribution of fixation times in one-step birth-death processes with two absorbing states. These are expressed in terms of the spectrum of the process, and we provide different representations as forward-only processes in eigenspace. These allow efficient sampling of fixation time distributions. As an application we study evolutionary game dynamics, where invading mutants can reach fixation or go extinct. We also highlight the median fixation time as a possible analog of mixing times in systems with small mutation rates and no absorbing states, whereas the mean fixation time has no such interpretation.

Cascading failures and the emergence of cooperation in evolutionary-game based models of social and economical networks.

PubMed

Wang, Wen-Xu; Lai, Ying-Cheng; Armbruster, Dieter

2011-09-01

We study catastrophic behaviors in large networked systems in the paradigm of evolutionary games by incorporating a realistic "death" or "bankruptcy" mechanism. We find that a cascading bankruptcy process can arise when defection strategies exist and individuals are vulnerable to deficit. Strikingly, we observe that, after the catastrophic cascading process terminates, cooperators are the sole survivors, regardless of the game types and of the connection patterns among individuals as determined by the topology of the underlying network. It is necessary that individuals cooperate with each other to survive the catastrophic failures. Cooperation thus becomes the optimal strategy and absolutely outperforms defection in the game evolution with respect to the "death" mechanism. Our results can be useful for understanding large-scale catastrophe in real-world systems and in particular, they may yield insights into significant social and economical phenomena such as large-scale failures of financial institutions and corporations during an economic recession.

Cascading failures and the emergence of cooperation in evolutionary-game based models of social and economical networks

NASA Astrophysics Data System (ADS)

Wang, Wen-Xu; Lai, Ying-Cheng; Armbruster, Dieter

2011-09-01

We study catastrophic behaviors in large networked systems in the paradigm of evolutionary games by incorporating a realistic "death" or "bankruptcy" mechanism. We find that a cascading bankruptcy process can arise when defection strategies exist and individuals are vulnerable to deficit. Strikingly, we observe that, after the catastrophic cascading process terminates, cooperators are the sole survivors, regardless of the game types and of the connection patterns among individuals as determined by the topology of the underlying network. It is necessary that individuals cooperate with each other to survive the catastrophic failures. Cooperation thus becomes the optimal strategy and absolutely outperforms defection in the game evolution with respect to the "death" mechanism. Our results can be useful for understanding large-scale catastrophe in real-world systems and in particular, they may yield insights into significant social and economical phenomena such as large-scale failures of financial institutions and corporations during an economic recession.

Games among relatives revisited.

PubMed

Allen, Benjamin; Nowak, Martin A

2015-08-07

We present a simple model for the evolution of social behavior in family-structured, finite sized populations. Interactions are represented as evolutionary games describing frequency-dependent selection. Individuals interact more frequently with siblings than with members of the general population, as quantified by an assortment parameter r, which can be interpreted as "relatedness". Other models, mostly of spatially structured populations, have shown that assortment can promote the evolution of cooperation by facilitating interaction between cooperators, but this effect depends on the details of the evolutionary process. For our model, we find that sibling assortment promotes cooperation in stringent social dilemmas such as the Prisoner's Dilemma, but not necessarily in other situations. These results are obtained through straightforward calculations of changes in gene frequency. We also analyze our model using inclusive fitness. We find that the quantity of inclusive fitness does not exist for general games. For special games, where inclusive fitness exists, it provides less information than the straightforward analysis. Copyright © 2015 Elsevier Ltd. All rights reserved.

Adaptive reproduction schedule as a cause of worker policing in social hymenoptera: a dynamic game analysis.

PubMed

Ohtsuki, Hisashi; Tsuji, Kazuki

2009-06-01

Evolutionary theories predict conflicts over sex allocation, male parentage, and reproductive allocation in hymenopteran societies. However, no theory to date has considered the evolution when a colony faces these three conflicts simultaneously. We tackled this issue by developing a dynamic game model, focusing especially on worker policing. Whereas a Nash equilibrium predicts male parentage patterns that are basically the same as those of relatedness-based worker-policing theory (queen multiple mating impedes worker reproduction), we also show the potential for worker policing under queen single mating. Worker policing will depend on the stage of colony growth that is caused by interaction with reproductive allocation conflict or a trade-off between current and future reproduction. Male production at an early stage greatly hinders the growth of the work force and undermines future inclusive fitness of colony members, leading to worker policing at the ergonomic stage. This new mechanism can explain much broader ranges of existing worker-policing behavior than that predicted from relatedness. Predictions differ in many respects from those of models assuming operation of only one or two of the three conflicts, suggesting the importance of interactions among conflicts.

Evolutionary Game Theory and Leadership

ERIC Educational Resources Information Center

Guastello, Stephen J.

2009-01-01

Comments on the article Leadership, followership, and evolution: Some lessons from the past by Van Vugt, Hogan, and Kaiser. This article offers a fresh perspective on leaders, followers, and their possible origins in nonhuman and primitive human behavior patterns. The connections between group coordination, leadership, and game theory have some…

The importance of mechanisms for the evolution of cooperation

PubMed Central

van den Berg, Pieter; Weissing, Franz J.

2015-01-01

Studies aimed at explaining the evolution of phenotypic traits have often solely focused on fitness considerations, ignoring underlying mechanisms. In recent years, there has been an increasing call for integrating mechanistic perspectives in evolutionary considerations, but it is not clear whether and how mechanisms affect the course and outcome of evolution. To study this, we compare four mechanistic implementations of two well-studied models for the evolution of cooperation, the Iterated Prisoner's Dilemma (IPD) game and the Iterated Snowdrift (ISD) game. Behavioural strategies are either implemented by a 1 : 1 genotype–phenotype mapping or by a simple neural network. Moreover, we consider two different scenarios for the effect of mutations. The same set of strategies is feasible in all four implementations, but the probability that a given strategy arises owing to mutation is largely dependent on the behavioural and genetic architecture. Our individual-based simulations show that this has major implications for the evolutionary outcome. In the ISD, different evolutionarily stable strategies are predominant in the four implementations, while in the IPD each implementation creates a characteristic dynamical pattern. As a consequence, the evolved average level of cooperation is also strongly dependent on the underlying mechanism. We argue that our findings are of general relevance for the evolution of social behaviour, pleading for the integration of a mechanistic perspective in models of social evolution. PMID:26246554

The coevolution of long-term pair bonds and cooperation.

PubMed

Song, Z; Feldman, M W

2013-05-01

The evolution of social traits may not only depend on but also change the social structure of the population. In particular, the evolution of pairwise cooperation, such as biparental care, depends on the pair-matching distribution of the population, and the latter often emerges as a collective outcome of individual pair-bonding traits, which are also under selection. Here, we develop an analytical model and individual-based simulations to study the coevolution of long-term pair bonds and cooperation in parental care, where partners play a Snowdrift game in each breeding season. We illustrate that long-term pair bonds may coevolve with cooperation when bonding cost is below a threshold. As long-term pair bonds lead to assortative interactions through pair-matching dynamics, they may promote the prevalence of cooperation. In addition to the pay-off matrix of a single game, the evolutionarily stable equilibrium also depends on bonding cost and accidental divorce rate, and it is determined by a form of balancing selection because the benefit from pair-bond maintenance diminishes as the frequency of cooperators increases. Our findings highlight the importance of ecological factors affecting social bonding cost and stability in understanding the coevolution of social behaviour and social structures, which may lead to the diversity of biological social systems. © 2013 The Authors. Journal of Evolutionary Biology © 2013 European Society For Evolutionary Biology.

Fourier decomposition of payoff matrix for symmetric three-strategy games.

PubMed

Szabó, György; Bodó, Kinga S; Allen, Benjamin; Nowak, Martin A

2014-10-01

In spatial evolutionary games the payoff matrices are used to describe pair interactions among neighboring players located on a lattice. Now we introduce a way how the payoff matrices can be built up as a sum of payoff components reflecting basic symmetries. For the two-strategy games this decomposition reproduces interactions characteristic to the Ising model. For the three-strategy symmetric games the Fourier components can be classified into four types representing games with self-dependent and cross-dependent payoffs, variants of three-strategy coordinations, and the rock-scissors-paper (RSP) game. In the absence of the RSP component the game is a potential game. The resultant potential matrix has been evaluated. The general features of these systems are analyzed when the game is expressed by the linear combinations of these components.

The emergence of cooperation from a single cooperative mutant

NASA Astrophysics Data System (ADS)

Cremer, Jonas; Melbinger, Anna; Frey, Erwin

2012-02-01

Population structure is one central condition which promotes the stability of cooperation: If cooperators more likely interact with other cooperators (positive assortment), they keep most of their benefit for themselves and are less exploited by non-cooperators. However, positive assortment can only act successfully if cooperation is already well established in the population such that cooperative individuals can successfully assort. But how can cooperation emerge when starting with a single cooperative mutant? Here we study this issue for a generic situation of microbial systems where microbes regularly form new colonies and show strong population growth. We show how and when the dynamical interplay between colony formation, population growth and evolution within colonies can provoke the emergence of cooperation. In particular, the probability for a single cooperative mutant to succeed is robustly large when colony-formation is fast or comparable to the time-scale of growth within colonies; growth supports cooperation.[4pt] [1] A. Melbinger, J. Cremer, and E. Frey, Evolutionary game theory in growing populations, Phys. Rev. Lett. 105, 178101 (2010)[0pt] [2] J. Cremer, A. Melbinger, and E. Frey, Evolutionary and population dynamics: a coupled approach, arXiv:1108.2604

Presence of a loner strain maintains cooperation and diversity in well-mixed bacterial communities.

PubMed

Inglis, R F; Biernaskie, J M; Gardner, A; Kümmerli, R

2016-01-13

Cooperation and diversity abound in nature despite cooperators risking exploitation from defectors and superior competitors displacing weaker ones. Understanding the persistence of cooperation and diversity is therefore a major problem for evolutionary ecology, especially in the context of well-mixed populations, where the potential for exploitation and displacement is greatest. Here, we demonstrate that a 'loner effect', described by economic game theorists, can maintain cooperation and diversity in real-world biological settings. We use mathematical models of public-good-producing bacteria to show that the presence of a loner strain, which produces an independent but relatively inefficient good, can lead to rock-paper-scissor dynamics, whereby cooperators outcompete loners, defectors outcompete cooperators and loners outcompete defectors. These model predictions are supported by our observations of evolutionary dynamics in well-mixed experimental communities of the bacterium Pseudomonas aeruginosa. We find that the coexistence of cooperators and defectors that produce and exploit, respectively, the iron-scavenging siderophore pyoverdine, is stabilized by the presence of loners with an independent iron-uptake mechanism. Our results establish the loner effect as a simple and general driver of cooperation and diversity in environments that would otherwise favour defection and the erosion of diversity. © 2016 The Authors.

Selfish punishment with avoiding mechanism can alleviate both first-order and second-order social dilemma.

PubMed

Cui, Pengbi; Wu, Zhi-Xi

2014-11-21

Punishment, especially selfish punishment, has recently been identified as a potent promoter in sustaining or even enhancing the cooperation among unrelated individuals. However, without other key mechanisms, the first-order social dilemma and second-order social dilemma are still two enduring conundrums in biology and the social sciences even with the presence of punishment. In the present study, we investigate a spatial evolutionary four-strategy prisoner׳s dilemma game model with avoiding mechanism, where the four strategies are cooperation, defection, altruistic and selfish punishment. By introducing the low level of random mutation of strategies, we demonstrate that the presence of selfish punishment with avoiding mechanism can alleviate the two kinds of social dilemmas for various parametrizations. In addition, we propose an extended pair approximation method, whose solutions can essentially estimate the dynamical behaviors and final evolutionary frequencies of the four strategies. At last, considering the analogy between our model and the classical Lotka-Volterra system, we introduce interaction webs based on the spatial replicator dynamics and the transformed payoff matrix to qualitatively characterize the emergent co-exist strategy phases, and its validity are supported by extensive simulations. Copyright © 2014 Elsevier Ltd. All rights reserved.

Evolution of cooperation in spatial iterated Prisoner's Dilemma games under localized extremal dynamics

NASA Astrophysics Data System (ADS)

Wang, Zhen; Yu, Chao; Cui, Guang-Hai; Li, Ya-Peng; Li, Ming-Chu

2016-02-01

The spatial Iterated Prisoner's Dilemma game has been widely studied in order to explain the evolution of cooperation. Considering the large strategy space size and infinite interaction times, it is unrealistic to adopt the common imitate-best updating rule, which assumes that the human players have much stronger abilities to recognize their neighbors' strategies than they do in the one-shot game. In this paper, a novel localized extremal dynamic system is proposed, in which each player only needs to recognize the payoff of his neighbors and changes his strategy randomly when he receives the lowest payoff in his neighborhood. The evolution of cooperation is here explored under this updating rule for neighborhoods of different sizes, which are characterized by their corresponding radiuses r. The results show that when r = 1, the system is trapped in a checkerboard-like state, where half of the players consistently use AllD-like strategies and the other half constantly change their strategies. When r = 2, the system first enters an AllD-like state, from which it escapes, and finally evolves to a TFT-like state. When r is larger, the system locks in a situation with similar low average fitness as r = 1. The number of active players and the ability to form clusters jointly distinguish the evolutionary processes for different values of r from each other. The current findings further provide some insight into the evolution of cooperation and collective behavior in biological and social systems.

Iterated Prisoner’s Dilemma contains strategies that dominate any evolutionary opponent

PubMed Central

Press, William H.; Dyson, Freeman J.

2012-01-01

The two-player Iterated Prisoner’s Dilemma game is a model for both sentient and evolutionary behaviors, especially including the emergence of cooperation. It is generally assumed that there exists no simple ultimatum strategy whereby one player can enforce a unilateral claim to an unfair share of rewards. Here, we show that such strategies unexpectedly do exist. In particular, a player X who is witting of these strategies can (i) deterministically set her opponent Y’s score, independently of his strategy or response, or (ii) enforce an extortionate linear relation between her and his scores. Against such a player, an evolutionary player’s best response is to accede to the extortion. Only a player with a theory of mind about his opponent can do better, in which case Iterated Prisoner’s Dilemma is an Ultimatum Game. PMID:22615375

Environmental Noise Could Promote Stochastic Local Stability of Behavioral Diversity Evolution

NASA Astrophysics Data System (ADS)

Zheng, Xiu-Deng; Li, Cong; Lessard, Sabin; Tao, Yi

2018-05-01

In this Letter, we investigate stochastic stability in a two-phenotype evolutionary game model for an infinite, well-mixed population undergoing discrete, nonoverlapping generations. We assume that the fitness of a phenotype is an exponential function of its expected payoff following random pairwise interactions whose outcomes randomly fluctuate with time. We show that the stochastic local stability of a constant interior equilibrium can be promoted by the random environmental noise even if the system may display a complicated nonlinear dynamics. This result provides a new perspective for a better understanding of how environmental fluctuations may contribute to the evolution of behavioral diversity.

Coevolutionary dynamics of aspiration and strategy in spatial repeated public goods games

NASA Astrophysics Data System (ADS)

Wu, Te; Fu, Feng; Wang, Long

2018-06-01

The evolutionary dynamics remain largely unknown for spatial populations where individuals are more likely to interact repeatedly. Under this settings, individuals can make their decisions to cooperate or not based on the decisions previously adopted by others in their neighborhoods. Using repeated public goods game, we construct a spatial model and use a statistical physics approach to study the coevolutionary dynamics of aspiration and strategy. Individuals each have an aspiration towards the groups they are involved. According to the outcome of each group, individuals have assessment of whether their aspirations are satisfied. If satisfied, they cooperate next round. Otherwise, they switch to defecting. Results show threshold phenomenon for harsh collective dilemma: cooperators sticking to high levels of aspiration can prevail over defectors, while cooperators with other levels are invariably wiped out. When the collective dilemma is relaxed, cooperation is greatly facilitated by inducing a high level of diversity of aspiration. Snapshots further show the spatial patterns of how this coevolutionary process leads to the emergence of an optimal solution associated with aspiration level, whose corresponding strategy are most prevalent. This optimal solution lies in one and the highest aspiration level allowed, and depends on the intensity of the social dilemma. By removing the memory effect, our results also confirm that repeated interactions can promote cooperation, but to a limited degree.

Diversity in times of adversity: probabilistic strategies in microbial survival games.

PubMed

Wolf, Denise M; Vazirani, Vijay V; Arkin, Adam P

2005-05-21

Population diversification strategies are ubiquitous among microbes, encompassing random phase-variation (RPV) of pathogenic bacteria, viral latency as observed in some bacteriophage and HIV, and the non-genetic diversity of bacterial stress responses. Precise conditions under which these diversification strategies confer an advantage have not been well defined. We develop a model of population growth conditioned on dynamical environmental and cellular states. Transitions among cellular states, in turn, may be biased by possibly noisy readings of the environment from cellular sensors. For various types of environmental dynamics and cellular sensor capability, we apply game-theoretic analysis to derive the evolutionarily stable strategy (ESS) for an organism and determine when that strategy is diversification. We find that: (1) RPV, effecting a sort of Parrondo paradox wherein random alternations between losing strategies produce a winning strategy, is selected when transitions between different selective environments cannot be sensed, (2) optimal RPV cell switching rates are a function of environmental lifecycle asymmetries and environmental autocorrelation, (3) probabilistic diversification upon entering a new environment is selected when sensors can detect environmental transitions but have poor precision in identifying new environments, and (4) in the presence of excess additive noise, low-pass filtering is required for evolutionary stability. We show that even when RPV is not the ESS, it may minimize growth rate variance and the risk of extinction due to 'unlucky' environmental dynamics.

An Evolutionary Game Theory Model of Revision-Resistant Motivations and Strategic Reasoning

DTIC Science & Technology

2008-08-01

The model also is consistent with a number of findings on the nature of emotions and related forms of motivation. 15. SUBJECT TERMS...because human beings have some kinds of motivations that are not reducible to the economist’s traditional notion of ordered preferences. These...simulation is designed in light of the most current human subject research on a widely studied game: the Ultimatum Game. This allows us to test

Cooperation and charity in spatial public goods game under different strategy update rules

NASA Astrophysics Data System (ADS)

Li, Yixiao; Jin, Xiaogang; Su, Xianchuang; Kong, Fansheng; Peng, Chengbin

2010-03-01

Human cooperation can be influenced by other human behaviors and recent years have witnessed the flourishing of studying the coevolution of cooperation and punishment, yet the common behavior of charity is seldom considered in game-theoretical models. In this article, we investigate the coevolution of altruistic cooperation and egalitarian charity in spatial public goods game, by considering charity as the behavior of reducing inter-individual payoff differences. Our model is that, in each generation of the evolution, individuals play games first and accumulate payoff benefits, and then each egalitarian makes a charity donation by payoff transfer in its neighborhood. To study the individual-level evolutionary dynamics, we adopt different strategy update rules and investigate their effects on charity and cooperation. These rules can be classified into two global rules: random selection rule in which individuals randomly update strategies, and threshold selection rule where only those with payoffs below a threshold update strategies. Simulation results show that random selection enhances the cooperation level, while threshold selection lowers the threshold of the multiplication factor to maintain cooperation. When charity is considered, it is incapable in promoting cooperation under random selection, whereas it promotes cooperation under threshold selection. Interestingly, the evolution of charity strongly depends on the dispersion of payoff acquisitions of the population, which agrees with previous results. Our work may shed light on understanding human egalitarianism.

Small groups and long memories promote cooperation.

PubMed

Stewart, Alexander J; Plotkin, Joshua B

2016-06-01

Complex social behaviors lie at the heart of many of the challenges facing evolutionary biology, sociology, economics, and beyond. For evolutionary biologists the question is often how group behaviors such as collective action, or decision making that accounts for memories of past experience, can emerge and persist in an evolving system. Evolutionary game theory provides a framework for formalizing these questions and admitting them to rigorous study. Here we develop such a framework to study the evolution of sustained collective action in multi-player public-goods games, in which players have arbitrarily long memories of prior rounds of play and can react to their experience in an arbitrary way. We construct a coordinate system for memory-m strategies in iterated n-player games that permits us to characterize all cooperative strategies that resist invasion by any mutant strategy, and stabilize cooperative behavior. We show that, especially when groups are small, longer-memory strategies make cooperation easier to evolve, by increasing the number of ways to stabilize cooperation. We also explore the co-evolution of behavior and memory. We find that even when memory has a cost, longer-memory strategies often evolve, which in turn drives the evolution of cooperation, even when the benefits for cooperation are low.

The coevolution of recognition and social behavior.

PubMed

Smead, Rory; Forber, Patrick

2016-05-26

Recognition of behavioral types can facilitate the evolution of cooperation by enabling altruistic behavior to be directed at other cooperators and withheld from defectors. While much is known about the tendency for recognition to promote cooperation, relatively little is known about whether such a capacity can coevolve with the social behavior it supports. Here we use evolutionary game theory and multi-population dynamics to model the coevolution of social behavior and recognition. We show that conditional harming behavior enables the evolution and stability of social recognition, whereas conditional helping leads to a deterioration of recognition ability. Expanding the model to include a complex game where both helping and harming interactions are possible, we find that conditional harming behavior can stabilize recognition, and thereby lead to the evolution of conditional helping. Our model identifies a novel hypothesis for the evolution of cooperation: conditional harm may have coevolved with recognition first, thereby helping to establish the mechanisms necessary for the evolution of cooperation.

The coevolution of recognition and social behavior

PubMed Central

Smead, Rory; Forber, Patrick

2016-01-01

Recognition of behavioral types can facilitate the evolution of cooperation by enabling altruistic behavior to be directed at other cooperators and withheld from defectors. While much is known about the tendency for recognition to promote cooperation, relatively little is known about whether such a capacity can coevolve with the social behavior it supports. Here we use evolutionary game theory and multi-population dynamics to model the coevolution of social behavior and recognition. We show that conditional harming behavior enables the evolution and stability of social recognition, whereas conditional helping leads to a deterioration of recognition ability. Expanding the model to include a complex game where both helping and harming interactions are possible, we find that conditional harming behavior can stabilize recognition, and thereby lead to the evolution of conditional helping. Our model identifies a novel hypothesis for the evolution of cooperation: conditional harm may have coevolved with recognition first, thereby helping to establish the mechanisms necessary for the evolution of cooperation. PMID:27225673

Evolution of flexibility and rigidity in retaliatory punishment

PubMed Central

MacGlashan, James; Littman, Michael L.

2017-01-01

Natural selection designs some social behaviors to depend on flexible learning processes, whereas others are relatively rigid or reflexive. What determines the balance between these two approaches? We offer a detailed case study in the context of a two-player game with antisocial behavior and retaliatory punishment. We show that each player in this game—a “thief” and a “victim”—must balance two competing strategic interests. Flexibility is valuable because it allows adaptive differentiation in the face of diverse opponents. However, it is also risky because, in competitive games, it can produce systematically suboptimal behaviors. Using a combination of evolutionary analysis, reinforcement learning simulations, and behavioral experimentation, we show that the resolution to this tension—and the adaptation of social behavior in this game—hinges on the game’s learning dynamics. Our findings clarify punishment’s adaptive basis, offer a case study of the evolution of social preferences, and highlight an important connection between natural selection and learning in the resolution of social conflicts. PMID:28893996

Evolution of Cooperation in Public Goods Games

NASA Astrophysics Data System (ADS)

Xia, Cheng-Yi; Zhang, Juan-Juan; Wang, Yi-Ling; Wang, Jin-Song

2011-10-01

We investigate the evolution of cooperation with evolutionary public goods games based on finite populations, where four pure strategies: cooperators, defectors, punishers and loners who are unwilling to participate are considered. By adopting approximate best response dynamics, we show that the magnitude of rationality not only quantitatively explains the experiment results in [Nature (London) 425 (2003) 390], but also it will heavily influence the evolution of cooperation. Compared with previous results of infinite populations, which result in two equilibriums, we show that there merely exists a special equilibrium and the relevant high value of bounded rationality will sustain cooperation. In addition, we characterize that loner's payoff plays an active role in the maintenance of cooperation, which will only be warranted for the low and moderate values of loner's payoff. It thus indicates the effects of rationality and loner's payoff will influence the cooperation. Finally, we highlight the important result that the introduction of voluntary participation and punishment will facilitate cooperation greatly.

Evolutionary construction by staying together and coming together.

PubMed

Tarnita, Corina E; Taubes, Clifford H; Nowak, Martin A

2013-03-07

The evolutionary trajectory of life on earth is one of increasing size and complexity. Yet the standard equations of evolutionary dynamics describe mutation and selection among similar organisms that compete on the same level of organization. Here we begin to outline a mathematical theory that might help to explore how evolution can be constructive, how natural selection can lead from lower to higher levels of organization. We distinguish two fundamental operations, which we call 'staying together' and 'coming together'. Staying together means that individuals form larger units by not separating after reproduction, while coming together means that independent individuals form aggregates. Staying together can lead to specialization and division of labor, but the developmental program must evolve in the basic unit. Coming together can be creative by combining units with different properties. Both operations have been identified in the context of multicellularity, but they have been treated very similarly. Here we point out that staying together and coming together can be found at every level of biological construction and moreover that they face different evolutionary problems. The distinction is particularly clear in the context of cooperation and defection. For staying together the stability of cooperation takes the form of a developmental error threshold, while coming together leads to evolutionary games and requires a mechanism for the evolution of cooperation. We use our models to discuss simple aspects of the evolution of protocells, eukarya, multi-cellularity and animal societies. Copyright © 2012 Elsevier Ltd. All rights reserved.

Anisotropic invasion and its consequences in two-strategy evolutionary games on a square lattice

NASA Astrophysics Data System (ADS)

Szabó, György; Varga, Levente; Szabó, Mátyás

2016-11-01

We have studied invasion processes in two-strategy evolutionary games on a square lattice for imitation rule when the players interact with their nearest neighbors. Monte Carlo simulations are performed for systems where the pair interactions are composed of a unit strength coordination game when varying the strengths of the self-dependent and cross-dependent components at a fixed noise level. The visualization of strategy distributions has clearly indicated that circular homogeneous domains evolve into squares with an orientation dependent on the composition. This phenomenon is related to the anisotropy of invasion velocities along the interfaces separating the two homogeneous regions. The quantified invasion velocities indicate the existence of a parameter region in which the invasions are opposite for the horizontal (or vertical) and the tilted interfaces. In this parameter region faceted islands of both strategies shrink and the system evolves from a random initial state into the homogeneous state that first percolated.

Evolution of cooperation in Axelrod tournament using cellular automata

NASA Astrophysics Data System (ADS)

Schimit, P. H. T.; Santos, B. O.; Soares, C. A.

2015-11-01

Results of the Axelrod Tournament were published in 1981, and since then, evolutionary game theory emerged as an idea for understanding relations, like conflict and cooperation, between rational decision-makers. Robert Axelrod organized it as a round-robin tournament where strategies for iterated Prisoner's Dilemma were faced in a sequence of two players game. Here, we attempt to simulate the strategies submitted to the tournament in a multi-agent context, where individuals play a two-player game with their neighbors. Each individual has one of the strategies, and it plays the Prisoner's Dilemma with its neighbors. According to actions chosen (cooperate or defect), points of life are subtracted from their profiles. When an individual dies, some fitness functions are defined to choose the most successful strategy which the new individual will copy. Although tit-for-tat was the best strategy, on average, in the tournament, in our evolutionary multi-agent context, it has not been successful.

Evolutionary fate of memory-one strategies in repeated prisoner's dilemma game in structured populations

NASA Astrophysics Data System (ADS)

Liu, Xu-Sheng; Wu, Zhi-Xi; Chen, Michael Z. Q.; Guan, Jian-Yue

2017-07-01

We study evolutionary spatial prisoner's dilemma game involving a one-step memory mechanism of the individuals whenever making strategy updating. In particular, during the process of strategy updating, each individual keeps in mind all the outcome of the action pairs adopted by himself and each of his neighbors in the last interaction, and according to which the individuals decide what actions they will take in the next round. Computer simulation results imply that win-stay-lose-shift like strategy win out of the memory-one strategy set in the stationary state. This result is robust in a large range of the payoff parameter, and does not depend on the initial state of the system. Furthermore, theoretical analysis with mean field and quasi-static approximation predict the same result. Thus, our studies suggest that win-stay-lose-shift like strategy is a stable dominant strategy in repeated prisoner's dilemma game in homogeneous structured populations.

Efficiency in evolutionary games: Darwin, Nash and the secret handshake.

PubMed

Robson, A J

1990-06-07

This paper considers any evolutionary game possessing several evolutionarily stable strategies, or ESSs, with differing payoffs. A mutant is introduced which will "destroy" any ESS which yields a lower payoff than another. This mutant possesses a costless signal and also conditions on the presence of this signal in each opponent. The mutant then can protect itself against a population playing an inefficient ESS by matching this against these non-signalers. At the same time, the mutants can achieve the more efficient ESS against the signaling mutant population itself. This construction is illustrated by means of the simplest possible example, a co-ordination game. The one-shot prisoner's dilemma is used to illustrate how a superior outcome which is not induced by an ESS may be temporarily but not permanently attained. In the case of the repeated prisoner's dilemma, the present argument seems to render the "evolution of co-operation" ultimately inevitable.

Pattern formation in individual-based systems with time-varying parameters

NASA Astrophysics Data System (ADS)

Ashcroft, Peter; Galla, Tobias

2013-12-01

We study the patterns generated in finite-time sweeps across symmetry-breaking bifurcations in individual-based models. Similar to the well-known Kibble-Zurek scenario of defect formation, large-scale patterns are generated when model parameters are varied slowly, whereas fast sweeps produce a large number of small domains. The symmetry breaking is triggered by intrinsic noise, originating from the discrete dynamics at the microlevel. Based on a linear-noise approximation, we calculate the characteristic length scale of these patterns. We demonstrate the applicability of this approach in a simple model of opinion dynamics, a model in evolutionary game theory with a time-dependent fitness structure, and a model of cell differentiation. Our theoretical estimates are confirmed in simulations. In further numerical work, we observe a similar phenomenon when the symmetry-breaking bifurcation is triggered by population growth.

Interactive diversity promotes the evolution of cooperation in structured populations

NASA Astrophysics Data System (ADS)

Su, Qi; Li, Aming; Zhou, Lei; Wang, Long

2016-10-01

Evolutionary games on networks traditionally assume that each individual adopts an identical strategy to interact with all its neighbors in each generation. Considering the prevalent diversity of individual interactions in the real society, here we propose the concept of interactive diversity, which allows individuals to adopt different strategies against different neighbors in each generation. We investigate the evolution of cooperation based on the edge dynamics rather than the traditional nodal dynamics in networked systems. The results show that, without invoking any other mechanisms, interactive diversity drives the frequency of cooperation to a high level for a wide range of parameters in both well-mixed and structured populations. Even in highly connected populations, cooperation still thrives. When interactive diversity and large topological heterogeneity are combined together, however, in the relaxed social dilemma, cooperation level is lower than that with just one of them, implying that the combination of many promotive factors may make a worse outcome. By an analytical approximation, we get the condition under which interactive diversity provides more advantages for cooperation than traditional evolutionary dynamics does. Numerical simulations validating the approximation are also presented. Our work provides a new line to explore the latent relation between the ubiquitous cooperation and individuals’ distinct responses in different interactions. The presented results suggest that interactive diversity should receive more attention in pursuing mechanisms fostering cooperation.

Four classes of interactions for evolutionary games.

PubMed

Szabó, György; Bodó, Kinga S; Allen, Benjamin; Nowak, Martin A

2015-08-01

The symmetric four-strategy games are decomposed into a linear combination of 16 basis games represented by orthogonal matrices. Among these basis games four classes can be distinguished as it is already found for the three-strategy games. The games with self-dependent (cross-dependent) payoffs are characterized by matrices consisting of uniform rows (columns). Six of 16 basis games describe coordination-type interactions among the strategy pairs and three basis games span the parameter space of the cyclic components that are analogous to the rock-paper-scissors games. In the absence of cyclic components the game is a potential game and the potential matrix is evaluated. The main features of the four classes of games are discussed separately and we illustrate some characteristic strategy distributions on a square lattice in the low noise limit if logit rule controls the strategy evolution. Analysis of the general properties indicates similar types of interactions at larger number of strategies for the symmetric matrix games.

Towards a richer evolutionary game theory

PubMed Central

McNamara, John M.

2013-01-01

Most examples of the application of evolutionary game theory to problems in biology involve highly simplified models. I contend that it is time to move on and include much more richness in models. In particular, more thought needs to be given to the importance of (i) between-individual variation; (ii) the interaction between individuals, and hence the process by which decisions are reached; (iii) the ecological and life-history context of the situation; (iv) the traits that are under selection, and (v) the underlying psychological mechanisms that lead to behaviour. I give examples where including variation between individuals fundamentally changes predicted outcomes of a game. Variation also selects for real-time responses, again resulting in changed outcomes. Variation can select for other traits, such as choosiness and social sensitivity. More generally, many problems involve coevolution of more than one trait. I identify situations where a reductionist approach, in which a game is isolated from is ecological setting, can be misleading. I also highlight the need to consider flexibility of behaviour, mental states and other issues concerned with the evolution of mechanism. PMID:23966616

Strategy evolution driven by switching probabilities in structured multi-agent systems

NASA Astrophysics Data System (ADS)

Zhang, Jianlei; Chen, Zengqiang; Li, Zhiqi

2017-10-01

Evolutionary mechanism driving the commonly seen cooperation among unrelated individuals is puzzling. Related models for evolutionary games on graphs traditionally assume that players imitate their successful neighbours with higher benefits. Notably, an implicit assumption here is that players are always able to acquire the required pay-off information. To relax this restrictive assumption, a contact-based model has been proposed, where switching probabilities between strategies drive the strategy evolution. However, the explicit and quantified relation between a player's switching probability for her strategies and the number of her neighbours remains unknown. This is especially a key point in heterogeneously structured system, where players may differ in the numbers of their neighbours. Focusing on this, here we present an augmented model by introducing an attenuation coefficient and evaluate its influence on the evolution dynamics. Results show that the individual influence on others is negatively correlated with the contact numbers specified by the network topologies. Results further provide the conditions under which the coexisting strategies can be calculated analytically.

Cultural selection drives the evolution of human communication systems

PubMed Central

Tamariz, Monica; Ellison, T. Mark; Barr, Dale J.; Fay, Nicolas

2014-01-01

Human communication systems evolve culturally, but the evolutionary mechanisms that drive this evolution are not well understood. Against a baseline that communication variants spread in a population following neutral evolutionary dynamics (also known as drift models), we tested the role of two cultural selection models: coordination- and content-biased. We constructed a parametrized mixed probabilistic model of the spread of communicative variants in four 8-person laboratory micro-societies engaged in a simple communication game. We found that selectionist models, working in combination, explain the majority of the empirical data. The best-fitting parameter setting includes an egocentric bias and a content bias, suggesting that participants retained their own previously used communicative variants unless they encountered a superior (content-biased) variant, in which case it was adopted. This novel pattern of results suggests that (i) a theory of the cultural evolution of human communication systems must integrate selectionist models and (ii) human communication systems are functionally adaptive complex systems. PMID:24966310

Cultural selection drives the evolution of human communication systems.

PubMed

Tamariz, Monica; Ellison, T Mark; Barr, Dale J; Fay, Nicolas

2014-08-07

Human communication systems evolve culturally, but the evolutionary mechanisms that drive this evolution are not well understood. Against a baseline that communication variants spread in a population following neutral evolutionary dynamics (also known as drift models), we tested the role of two cultural selection models: coordination- and content-biased. We constructed a parametrized mixed probabilistic model of the spread of communicative variants in four 8-person laboratory micro-societies engaged in a simple communication game. We found that selectionist models, working in combination, explain the majority of the empirical data. The best-fitting parameter setting includes an egocentric bias and a content bias, suggesting that participants retained their own previously used communicative variants unless they encountered a superior (content-biased) variant, in which case it was adopted. This novel pattern of results suggests that (i) a theory of the cultural evolution of human communication systems must integrate selectionist models and (ii) human communication systems are functionally adaptive complex systems.

Evolution of cooperation with shared costs and benefits

PubMed Central

Brown, Joel S; Vincent, Thomas L

2008-01-01

The quest to determine how cooperation evolves can be based on evolutionary game theory, in spite of the fact that evolutionarily stable strategies (ESS) for most non-zero-sum games are not cooperative. We analyse the evolution of cooperation for a family of evolutionary games involving shared costs and benefits with a continuum of strategies from non-cooperation to total cooperation. This cost–benefit game allows the cooperator to share in the benefit of a cooperative act, and the recipient to be burdened with a share of the cooperator's cost. The cost–benefit game encompasses the Prisoner's Dilemma, Snowdrift game and Partial Altruism. The models produce ESS solutions of total cooperation, partial cooperation, non-cooperation and coexistence between cooperation and non-cooperation. Cooperation emerges from an interplay between the nonlinearities in the cost and benefit functions. If benefits increase at a decelerating rate and costs increase at an accelerating rate with the degree of cooperation, then the ESS has an intermediate level of cooperation. The game also exhibits non-ESS points such as unstable minima, convergent-stable minima and unstable maxima. The emergence of cooperative behaviour in this game represents enlightened self-interest, whereas non-cooperative solutions illustrate the Tragedy of the Commons. Games having either a stable maximum or a stable minimum have the property that small changes in the incentive structure (model parameter values) or culture (starting frequencies of strategies) result in correspondingly small changes in the degree of cooperation. Conversely, with unstable maxima or unstable minima, small changes in the incentive structure or culture can result in a switch from non-cooperation to total cooperation (and vice versa). These solutions identify when human or animal societies have the potential for cooperation and whether cooperation is robust or fragile. PMID:18495622

A Five-Species Jungle Game.

PubMed

Kang, Yibin; Pan, Qiuhui; Wang, Xueting; He, Mingfeng

2016-01-01

In this paper, we investigate the five-species Jungle game in the framework of evolutionary game theory. We address the coexistence and biodiversity of the system using mean-field theory and Monte Carlo simulations. Then, we find that the inhibition from the bottom-level species to the top-level species can be critical factors that affect biodiversity, no matter how it is distributed, whether homogeneously well mixed or structured. We also find that predators' different preferences for food affect species' coexistence.

Critical Behavior of Spatial Evolutionary Game with Altruistic to Spiteful Preferences on Two-Dimensional Lattices

NASA Astrophysics Data System (ADS)

Yang, Bo; Li, Xiao-Teng; Chen, Wei; Liu, Jian; Chen, Xiao-Song

2016-10-01

Self-questioning mechanism which is similar to single spin-flip of Ising model in statistical physics is introduced into spatial evolutionary game model. We propose a game model with altruistic to spiteful preferences via weighted sums of own and opponent's payoffs. This game model can be transformed into Ising model with an external field. Both interaction between spins and the external field are determined by the elements of payoff matrix and the preference parameter. In the case of perfect rationality at zero social temperature, this game model has three different phases which are entirely cooperative phase, entirely non-cooperative phase and mixed phase. In the investigations of the game model with Monte Carlo simulation, two paths of payoff and preference parameters are taken. In one path, the system undergoes a discontinuous transition from cooperative phase to non-cooperative phase with the change of preference parameter. In another path, two continuous transitions appear one after another when system changes from cooperative phase to non-cooperative phase with the prefenrence parameter. The critical exponents v, β, and γ of two continuous phase transitions are estimated by the finite-size scaling analysis. Both continuous phase transitions have the same critical exponents and they belong to the same universality class as the two-dimensional Ising model. Supported by the National Natural Science Foundation of China under Grant Nos. 11121403 and 11504384

Integrating evolutionary game theory into an agent-based model of ductal carcinoma in situ: Role of gap junctions in cancer progression.

PubMed

Malekian, Negin; Habibi, Jafar; Zangooei, Mohammad Hossein; Aghakhani, Hojjat

2016-11-01

There are many cells with various phenotypic behaviors in cancer interacting with each other. For example, an apoptotic cell may induce apoptosis in adjacent cells. A living cell can also protect cells from undergoing apoptosis and necrosis. These survival and death signals are propagated through interaction pathways between adjacent cells called gap junctions. The function of these signals depends on the cellular context of the cell receiving them. For instance, a receiver cell experiencing a low level of oxygen may interpret a received survival signal as an apoptosis signal. In this study, we examine the effect of these signals on tumor growth. We make an evolutionary game theory component in order to model the signal propagation through gap junctions. The game payoffs are defined as a function of cellular context. Then, the game theory component is integrated into an agent-based model of tumor growth. After that, the integrated model is applied to ductal carcinoma in situ, a type of early stage breast cancer. Different scenarios are explored to observe the impact of the gap junction communication and parameters of the game theory component on cancer progression. We compare these scenarios by using the Wilcoxon signed-rank test. The Wilcoxon signed-rank test succeeds in proving a significant difference between the tumor growth of the model before and after considering the gap junction communication. The Wilcoxon signed-rank test also proves that the tumor growth significantly depends on the oxygen threshold of turning survival signals into apoptosis. In this study, the gap junction communication is modeled by using evolutionary game theory to illustrate its role at early stage cancers such as ductal carcinoma in situ. This work indicates that the gap junction communication and the oxygen threshold of turning survival signals into apoptosis can notably affect cancer progression. Copyright © 2016 Elsevier Ireland Ltd. All rights reserved.

Game Theory Meets Wireless Sensor Networks Security Requirements and Threats Mitigation: A Survey.

PubMed

Abdalzaher, Mohamed S; Seddik, Karim; Elsabrouty, Maha; Muta, Osamu; Furukawa, Hiroshi; Abdel-Rahman, Adel

2016-06-29

We present a study of using game theory for protecting wireless sensor networks (WSNs) from selfish behavior or malicious nodes. Due to scalability, low complexity and disseminated nature of WSNs, malicious attacks can be modeled effectively using game theory. In this study, we survey the different game-theoretic defense strategies for WSNs. We present a taxonomy of the game theory approaches based on the nature of the attack, whether it is caused by an external attacker or it is the result of an internal node acting selfishly or maliciously. We also present a general trust model using game theory for decision making. We, finally, identify the significant role of evolutionary games for WSNs security against intelligent attacks; then, we list several prospect applications of game theory to enhance the data trustworthiness and node cooperation in different WSNs.

The Handicap Principle for Trust in Computer Security, the Semantic Web and Social Networking

NASA Astrophysics Data System (ADS)

Ma, Zhanshan (Sam); Krings, Axel W.; Hung, Chih-Cheng

Communication is a fundamental function of life, and it exists in almost all living things: from single-cell bacteria to human beings. Communication, together with competition and cooperation,arethree fundamental processes in nature. Computer scientists are familiar with the study of competition or 'struggle for life' through Darwin's evolutionary theory, or even evolutionary computing. They may be equally familiar with the study of cooperation or altruism through the Prisoner's Dilemma (PD) game. However, they are likely to be less familiar with the theory of animal communication. The objective of this article is three-fold: (i) To suggest that the study of animal communication, especially the honesty (reliability) of animal communication, in which some significant advances in behavioral biology have been achieved in the last three decades, should be on the verge to spawn important cross-disciplinary research similar to that generated by the study of cooperation with the PD game. One of the far-reaching advances in the field is marked by the publication of "The Handicap Principle: a Missing Piece of Darwin's Puzzle" by Zahavi (1997). The 'Handicap' principle [34][35], which states that communication signals must be costly in some proper way to be reliable (honest), is best elucidated with evolutionary games, e.g., Sir Philip Sidney (SPS) game [23]. Accordingly, we suggest that the Handicap principle may serve as a fundamental paradigm for trust research in computer science. (ii) To suggest to computer scientists that their expertise in modeling computer networks may help behavioral biologists in their study of the reliability of animal communication networks. This is largely due to the historical reason that, until the last decade, animal communication was studied with the dyadic paradigm (sender-receiver) rather than with the network paradigm. (iii) To pose several open questions, the answers to which may bear some refreshing insights to trust research in computer science, especially secure and resilient computing, the semantic web, and social networking. One important thread unifying the three aspects is the evolutionary game theory modeling or its extensions with survival analysis and agreement algorithms [19][20], which offer powerful game models for describing time-, space-, and covariate-dependent frailty (uncertainty and vulnerability) and deception (honesty).

Evolutionary Stability in the Traveler's Dilemma

ERIC Educational Resources Information Center

Barker, Andrew T.

2009-01-01

The traveler's dilemma is a generalization of the prisoner's dilemma which shows clearly a paradox of game theory. In the traveler's dilemma, the strategy chosen by analysis and theory seems obviously wrong intuitively. Here we develop a measure of evolutionary stability and show that the evolutionarily stable equilibrium is in some sense not very…

Evolutionary game theory using agent-based methods.

PubMed

Adami, Christoph; Schossau, Jory; Hintze, Arend

2016-12-01

Evolutionary game theory is a successful mathematical framework geared towards understanding the selective pressures that affect the evolution of the strategies of agents engaged in interactions with potential conflicts. While a mathematical treatment of the costs and benefits of decisions can predict the optimal strategy in simple settings, more realistic settings such as finite populations, non-vanishing mutations rates, stochastic decisions, communication between agents, and spatial interactions, require agent-based methods where each agent is modeled as an individual, carries its own genes that determine its decisions, and where the evolutionary outcome can only be ascertained by evolving the population of agents forward in time. While highlighting standard mathematical results, we compare those to agent-based methods that can go beyond the limitations of equations and simulate the complexity of heterogeneous populations and an ever-changing set of interactors. We conclude that agent-based methods can predict evolutionary outcomes where purely mathematical treatments cannot tread (for example in the weak selection-strong mutation limit), but that mathematics is crucial to validate the computational simulations. Copyright © 2016 Elsevier B.V. All rights reserved.

The evolution of prompt reaction to adverse ties.

PubMed

Van Segbroeck, Sven; Santos, Francisco C; Nowé, Ann; Pacheco, Jorge M; Lenaerts, Tom

2008-10-17

In recent years it has been found that the combination of evolutionary game theory with population structures modelled in terms of dynamical graphs, in which individuals are allowed to sever unwanted social ties while keeping the good ones, provides a viable solution to the conundrum of cooperation. It is well known that in reality individuals respond differently to disadvantageous interactions. Yet, the evolutionary mechanism determining the individuals' willingness to sever unfavourable ties remains unclear. We introduce a novel way of thinking about the joint evolution of cooperation and social contacts. The struggle for survival between cooperators and defectors leads to an arms race for swiftness in adjusting social ties, based purely on a self-regarding, individual judgement. Since defectors are never able to establish social ties under mutual agreement, they break adverse ties more rapidly than cooperators, who tend to evolve stable and long-term relations. Ironically, defectors' constant search for partners to exploit leads to heterogeneous networks that improve the survivability of cooperators, compared to the traditional homogenous population assumption. When communities face the prisoner's dilemma, swift reaction to adverse ties evolves when competition is fierce between cooperators and defectors, providing an evolutionary basis for the necessity of individuals to adjust their social ties. Our results show how our innate resilience to change relates to mutual agreement between cooperators and how "loyalty" or persistent social ties bring along an evolutionary disadvantage, both from an individual and group perspective.

Evolutionary graph theory: breaking the symmetry between interaction and replacement

PubMed Central

Ohtsuki, Hisashi; Pacheco, Jorge M.; Nowak, Martin A.

2008-01-01

We study evolutionary dynamics in a population whose structure is given by two graphs: the interaction graph determines who plays with whom in an evolutionary game; the replacement graph specifies the geometry of evolutionary competition and updating. First, we calculate the fixation probabilities of frequency dependent selection between two strategies or phenotypes. We consider three different update mechanisms: birth-death, death-birth and imitation. Then, as a particular example, we explore the evolution of cooperation. Suppose the interaction graph is a regular graph of degree h, the replacement graph is a regular graph of degree g and the overlap between the two graphs is a regular graph of degree l. We show that cooperation is favored by natural selection if b/c > hg/l. Here, b and c denote the benefit and cost of the altruistic act. This result holds for death-birth updating, weak selection and large population size. Note that the optimum population structure for cooperators is given by maximum overlap between the interaction and the replacement graph (g = h = l), which means that the two graphs are identical. We also prove that a modified replicator equation can describe how the expected values of the frequencies of an arbitrary number of strategies change on replacement and interaction graphs: the two graphs induce a transformation of the payoff matrix. PMID:17350049

Stags, Hawks, and Doves: Social Evolution Theory and Individual Variation in Cooperation.

PubMed

Van Cleve, Jeremy

2017-09-01

One of the triumphs of evolutionary biology is the discovery of robust mechanisms that promote the evolution of cooperative behaviors even when cooperation reduces the fertility or survival of cooperators. These mechanisms include, kin selection, reciprocity, and direct benefits to cooperation that are often nonlinear. Though they have been extensively studied separately, investigating the joint action of these mechanisms has been more difficult. Moreover, how these mechanisms shape variation in cooperation is not well known. Such variation is crucial for understanding the evolution of behavioral syndromes and animal personality. Here, I use the tools of kin selection and evolutionary game theory to build a framework that integrates these mechanisms for pairwise social interactions. Using relatedness as a measure of the strength of kin selection, responsiveness as a measure of reciprocity, and synergy as a measure of payoff nonlinearity, I show how different combinations of these three parameters produce directional selection for or against cooperation or variation in levels of cooperation via stabilizing or diversifying selection. Moreover, each of these outcomes maps uniquely to one of four classic games from evolutionary game theory, which means that modulating relatedness, responsiveness, and synergy effectively transforms the payoff matrix from one the evolutionary game to another. Assuming that cooperation exacts a fertility cost on cooperators and provides a fertility benefit to social partners, a prisoner's dilemma game and directional selection against cooperation occur when relatedness and responsiveness are low and synergy is not too positive. Enough positive synergy in these conditions generates a stag-hunt game and diversifying selection. High levels of relatedness or responsiveness turn cooperation from a fitness cost into a fitness benefit, which produces a mutualism game and directional selection for cooperation when synergy is not too negative. Sufficiently negative synergy in this case creates a hawk-dove game and stabilizing selection for cooperation. I extend the results with relatedness and synergy to social groups and show that how group size changes the effect of relatedness and synergy on selection for cooperation depends on how the per capita benefit of cooperation changes with group size. Together, these results provide a general framework with which to generate comparative predictions that can be tested using quantitative genetic techniques and experimental techniques that manipulate investment in cooperation. These predictions will help us understand both interspecific variation in cooperation as well as within-population and within-group variation in cooperation related to behavioral syndromes. © The Author 2017. Published by Oxford University Press on behalf of the Society for Integrative and Comparative Biology. All rights reserved. For permissions please email: journals.permissions@oup.com.

Combinatorial games with a pass: a dynamical systems approach.

PubMed

Morrison, Rebecca E; Friedman, Eric J; Landsberg, Adam S

2011-12-01

By treating combinatorial games as dynamical systems, we are able to address a longstanding open question in combinatorial game theory, namely, how the introduction of a "pass" move into a game affects its behavior. We consider two well known combinatorial games, 3-pile Nim and 3-row Chomp. In the case of Nim, we observe that the introduction of the pass dramatically alters the game's underlying structure, rendering it considerably more complex, while for Chomp, the pass move is found to have relatively minimal impact. We show how these results can be understood by recasting these games as dynamical systems describable by dynamical recursion relations. From these recursion relations, we are able to identify underlying structural connections between these "games with passes" and a recently introduced class of "generic (perturbed) games." This connection, together with a (non-rigorous) numerical stability analysis, allows one to understand and predict the effect of a pass on a game.

Quantum Prisoner’s Dilemma game on hypergraph networks

NASA Astrophysics Data System (ADS)

Pawela, Łukasz; Sładkowski, Jan

2013-02-01

We study the possible advantages of adopting quantum strategies in multi-player evolutionary games. We base our study on the three-player Prisoner’s Dilemma (PD) game. In order to model the simultaneous interaction between three agents we use hypergraphs and hypergraph networks. In particular, we study two types of networks: a random network and a SF-like network. The obtained results show that in the case of a three-player game on a hypergraph network, quantum strategies are not necessarily stochastically stable strategies. In some cases, the defection strategy can be as good as a quantum one.

Emergence of communities and diversity in social networks

PubMed Central

Han, Xiao; Cao, Shinan; Shen, Zhesi; Zhang, Boyu; Wang, Wen-Xu; Cressman, Ross

2017-01-01

Communities are common in complex networks and play a significant role in the functioning of social, biological, economic, and technological systems. Despite widespread interest in detecting community structures in complex networks and exploring the effect of communities on collective dynamics, a deep understanding of the emergence and prevalence of communities in social networks is still lacking. Addressing this fundamental problem is of paramount importance in understanding, predicting, and controlling a variety of collective behaviors in society. An elusive question is how communities with common internal properties arise in social networks with great individual diversity. Here, we answer this question using the ultimatum game, which has been a paradigm for characterizing altruism and fairness. We experimentally show that stable local communities with different internal agreements emerge spontaneously and induce social diversity into networks, which is in sharp contrast to populations with random interactions. Diverse communities and social norms come from the interaction between responders with inherent heterogeneous demands and rational proposers via local connections, where the former eventually become the community leaders. This result indicates that networks are significant in the emergence and stabilization of communities and social diversity. Our experimental results also provide valuable information about strategies for developing network models and theories of evolutionary games and social dynamics. PMID:28235785

Emergence of communities and diversity in social networks.

PubMed

Han, Xiao; Cao, Shinan; Shen, Zhesi; Zhang, Boyu; Wang, Wen-Xu; Cressman, Ross; Stanley, H Eugene

2017-03-14

Communities are common in complex networks and play a significant role in the functioning of social, biological, economic, and technological systems. Despite widespread interest in detecting community structures in complex networks and exploring the effect of communities on collective dynamics, a deep understanding of the emergence and prevalence of communities in social networks is still lacking. Addressing this fundamental problem is of paramount importance in understanding, predicting, and controlling a variety of collective behaviors in society. An elusive question is how communities with common internal properties arise in social networks with great individual diversity. Here, we answer this question using the ultimatum game, which has been a paradigm for characterizing altruism and fairness. We experimentally show that stable local communities with different internal agreements emerge spontaneously and induce social diversity into networks, which is in sharp contrast to populations with random interactions. Diverse communities and social norms come from the interaction between responders with inherent heterogeneous demands and rational proposers via local connections, where the former eventually become the community leaders. This result indicates that networks are significant in the emergence and stabilization of communities and social diversity. Our experimental results also provide valuable information about strategies for developing network models and theories of evolutionary games and social dynamics.

A Game-Theory Based Incentive Framework for an Intelligent Traffic System as Part of a Smart City Initiative.

PubMed

Mei, Haibo; Poslad, Stefan; Du, Shuang

2017-12-11

Intelligent Transportation Systems (ITSs) can be applied to inform and incentivize travellers to help them make cognizant choices concerning their trip routes and transport modality use for their daily travel whilst achieving more sustainable societal and transport authority goals. However, in practice, it is challenging for an ITS to enable incentive generation that is context-driven and personalized, whilst supporting multi-dimensional travel goals. This is because an ITS has to address the situation where different travellers have different travel preferences and constraints for route and modality, in the face of dynamically-varying traffic conditions. Furthermore, personalized incentive generation also needs to dynamically achieve different travel goals from multiple travellers, in the face of their conducts being a mix of both competitive and cooperative behaviours. To address this challenge, a Rule-based Incentive Framework (RIF) is proposed in this paper that utilizes both decision tree and evolutionary game theory to process travel information and intelligently generate personalized incentives for travellers. The travel information processed includes travellers' mobile patterns, travellers' modality preferences and route traffic volume information. A series of MATLAB simulations of RIF was undertaken to validate RIF to show that it is potentially an effective way to incentivize travellers to change travel routes and modalities as an essential smart city service.

Cooperation in spatial evolutionary games with historical payoffs

NASA Astrophysics Data System (ADS)

Wang, Xu-Wen; Nie, Sen; Jiang, Luo-Luo; Wang, Bing-Hong; Chen, Shi-Ming

2016-08-01

The most common of strategy adoption in evolutionary games relies on players' payoffs of the last round. While a rational player usually fixes the coming strategy by comprehensively considering certain amount of payoff information within its memory length. Here, we explore several measures of historical payoffs in getting the weighted average payoff. Then, player sets the strategy by comparing the weighted average payoff of neighbour's and itself. We show that, cooperators can resist the invasion by referring to the most payoff information, when strategy and measure coevolve. In contrast, strategy adoption of defectors only relies on the nearest one round. Especially, our results suggest that, excessive attention of past payoffs is not favorable to spread cooperative behaviors.

Phase diagrams for an evolutionary prisoner's dilemma game on two-dimensional lattices

NASA Astrophysics Data System (ADS)

Szabó, György; Vukov, Jeromos; Szolnoki, Attila

2005-10-01

The effects of payoffs and noise on the maintenance of cooperative behavior are studied in an evolutionary prisoner’s dilemma game with players located on the sites of different two-dimensional lattices. This system exhibits a phase transition from a mixed state of cooperators and defectors to a homogeneous one where only the defectors remain alive. Using Monte Carlo simulations and the generalized mean-field approximations we have determined the phase boundaries (critical points) separating the two phases on the plane of the temperature (noise) and temptation to choose defection. In the zero temperature limit the cooperation can be sustained only for those connectivity structures where three-site clique percolation occurs.

Investigation on Law and Economics Based on Complex Network and Time Series Analysis.

PubMed

Yang, Jian; Qu, Zhao; Chang, Hui

2015-01-01

The research focuses on the cooperative relationship and the strategy tendency among three mutually interactive parties in financing: small enterprises, commercial banks and micro-credit companies. Complex network theory and time series analysis were applied to figure out the quantitative evidence. Moreover, this paper built up a fundamental model describing the particular interaction among them through evolutionary game. Combining the results of data analysis and current situation, it is justifiable to put forward reasonable legislative recommendations for regulations on lending activities among small enterprises, commercial banks and micro-credit companies. The approach in this research provides a framework for constructing mathematical models and applying econometrics and evolutionary game in the issue of corporation financing.

A Five-Species Jungle Game

PubMed Central

Kang, Yibin; Pan, Qiuhui; Wang, Xueting; He, Mingfeng

2016-01-01

In this paper, we investigate the five-species Jungle game in the framework of evolutionary game theory. We address the coexistence and biodiversity of the system using mean-field theory and Monte Carlo simulations. Then, we find that the inhibition from the bottom-level species to the top-level species can be critical factors that affect biodiversity, no matter how it is distributed, whether homogeneously well mixed or structured. We also find that predators’ different preferences for food affect species’ coexistence. PMID:27332995

Hyperbolic scaling and computing in social crowds: Comment on "Human behaviours in evacuation crowd dynamics: From modelling to "big data" toward crisis management" by Nicola Bellomo et al.

NASA Astrophysics Data System (ADS)

Outada, Nisrine

2016-09-01

I have read with great interest the paper [5] where the authors present an overview and critical analysis of the literature on the modeling of the crowd dynamics with special attention to evacuation dynamics. The approach developed is based on suitable development of methods of the kinetic theory. Interactions, which lead to the decision choice, are modeled by theoretical tools of stochastic evolutionary game theory [11,12]. However, the paper [5] provides not only a survey focused on topics of great interest for our society, but also it looks ahead to a variety of interesting and challenging mathematical problems. Specifically, I am interested in the derivation of macroscopic (hydrodynamic) models from the underlying description given from the kinetic theory approach, more specifically by the kinetic theory for active particles [8]. A general reference on crowd modeling is the recently published book [10].

Game Theory Meets Wireless Sensor Networks Security Requirements and Threats Mitigation: A Survey

PubMed Central

Abdalzaher, Mohamed S.; Seddik, Karim; Elsabrouty, Maha; Muta, Osamu; Furukawa, Hiroshi; Abdel-Rahman, Adel

2016-01-01

We present a study of using game theory for protecting wireless sensor networks (WSNs) from selfish behavior or malicious nodes. Due to scalability, low complexity and disseminated nature of WSNs, malicious attacks can be modeled effectively using game theory. In this study, we survey the different game-theoretic defense strategies for WSNs. We present a taxonomy of the game theory approaches based on the nature of the attack, whether it is caused by an external attacker or it is the result of an internal node acting selfishly or maliciously. We also present a general trust model using game theory for decision making. We, finally, identify the significant role of evolutionary games for WSNs security against intelligent attacks; then, we list several prospect applications of game theory to enhance the data trustworthiness and node cooperation in different WSNs. PMID:27367700

Effect of a large gaming neighborhood and a strategy adaptation neighborhood for bolstering network reciprocity in a prisoner's dilemma game

NASA Astrophysics Data System (ADS)

Ogasawara, Takashi; Tanimoto, Jun; Fukuda, Eriko; Hagishima, Aya; Ikegaya, Naoki

2014-12-01

In 2 × 2 prisoner's dilemma (PD) games, network reciprocity is one mechanism for adding social viscosity, leading to a cooperative equilibrium. In this paper, we explain how gaming neighborhoods and strategy-adaptation neighborhoods affect network reciprocity independently in spatial PD games. We explore an appropriate range of strategy adaptation neighborhoods as opposed to the conventional method of making the gaming and strategy adaptation neighborhoods coincide to enhance the level of cooperation. In cases of expanding gaming neighborhoods, network reciprocity falls to a low level relative to the conventional setting. In the discussion below, which is based on the results of our simulation, we explore how these enhancements come about. Essentially, varying the range of the neighborhoods influences how cooperative clusters form and expand in the evolutionary process.

The Genetic Precursors and the Advantageous and Disadvantageous Sequelae of Inhibited Temperament: An Evolutionary Perspective

ERIC Educational Resources Information Center

Davies, Patrick T.; Cicchetti, Dante; Hentges, Rochelle F.; Sturge-Apple, Melissa L.

2013-01-01

Guided by evolutionary game theory (Korte, Koolhaas, Wingfield, & McEwen, 2005), this study aimed to identify the genetic precursors and the psychosocial sequelae of inhibited temperament in a sociodemographically disadvantaged and racially diverse sample (N = 201) of 2-year-old children who experienced elevated levels of domestic violence.…

The evolution of reciprocity in sizable human groups.

PubMed

Rothschild, Casey G

2009-04-21

The scale and complexity of human cooperation is an important and unresolved evolutionary puzzle. This article uses the finitely repeated n person Prisoners' Dilemma game to illustrate how sapience can greatly enhance group-selection effects and lead to the evolutionary stability of cooperation in large groups. This affords a simple and direct explanation of the human "exception".

The Evolution of Generosity in the Ultimatum Game

PubMed Central

Hintze, Arend; Hertwig, Ralph

2016-01-01

When humans fail to make optimal decisions in strategic games and economic gambles, researchers typically try to explain why that behaviour is biased. To this end, they search for mechanisms that cause human behaviour to deviate from what seems to be the rational optimum. But perhaps human behaviour is not biased; perhaps research assumptions about the optimality of strategies are incomplete. In the one-shot anonymous symmetric ultimatum game (UG), humans fail to play optimally as defined by the Nash equilibrium. However, the distinction between kin and non-kin—with kin detection being a key evolutionary adaption—is often neglected when deriving the “optimal” strategy. We computationally evolved strategies in the UG that were equipped with an evolvable probability to discern kin from non-kin. When an opponent was not kin, agents evolved strategies that were similar to those used by humans. We therefore conclude that the strategy humans play is not irrational. The deviation between behaviour and the Nash equilibrium may rather be attributable to key evolutionary adaptations, such as kin detection. Our findings further suggest that social preference models are likely to capture mechanisms that permit people to play optimally in an evolutionary context. Once this context is taken into account, human behaviour no longer appears irrational. PMID:27677330

The Evolution of Generosity in the Ultimatum Game.

PubMed

Hintze, Arend; Hertwig, Ralph

2016-09-28

When humans fail to make optimal decisions in strategic games and economic gambles, researchers typically try to explain why that behaviour is biased. To this end, they search for mechanisms that cause human behaviour to deviate from what seems to be the rational optimum. But perhaps human behaviour is not biased; perhaps research assumptions about the optimality of strategies are incomplete. In the one-shot anonymous symmetric ultimatum game (UG), humans fail to play optimally as defined by the Nash equilibrium. However, the distinction between kin and non-kin-with kin detection being a key evolutionary adaption-is often neglected when deriving the "optimal" strategy. We computationally evolved strategies in the UG that were equipped with an evolvable probability to discern kin from non-kin. When an opponent was not kin, agents evolved strategies that were similar to those used by humans. We therefore conclude that the strategy humans play is not irrational. The deviation between behaviour and the Nash equilibrium may rather be attributable to key evolutionary adaptations, such as kin detection. Our findings further suggest that social preference models are likely to capture mechanisms that permit people to play optimally in an evolutionary context. Once this context is taken into account, human behaviour no longer appears irrational.

Basins of coexistence and extinction in spatially extended ecosystems of cyclically competing species.

PubMed

Ni, Xuan; Yang, Rui; Wang, Wen-Xu; Lai, Ying-Cheng; Grebogi, Celso

2010-12-01

Microscopic models based on evolutionary games on spatially extended scales have recently been developed to address the fundamental issue of species coexistence. In this pursuit almost all existing works focus on the relevant dynamical behaviors originated from a single but physically reasonable initial condition. To gain comprehensive and global insights into the dynamics of coexistence, here we explore the basins of coexistence and extinction and investigate how they evolve as a basic parameter of the system is varied. Our model is cyclic competitions among three species as described by the classical rock-paper-scissors game, and we consider both discrete lattice and continuous space, incorporating species mobility and intraspecific competitions. Our results reveal that, for all cases considered, a basin of coexistence always emerges and persists in a substantial part of the parameter space, indicating that coexistence is a robust phenomenon. Factors such as intraspecific competition can, in fact, promote coexistence by facilitating the emergence of the coexistence basin. In addition, we find that the extinction basins can exhibit quite complex structures in terms of the convergence time toward the final state for different initial conditions. We have also developed models based on partial differential equations, which yield basin structures that are in good agreement with those from microscopic stochastic simulations. To understand the origin and emergence of the observed complicated basin structures is challenging at the present due to the extremely high dimensional nature of the underlying dynamical system. © 2010 American Institute of Physics.

Evolutionary dynamics of collective action in spatially structured populations.

PubMed

Peña, Jorge; Nöldeke, Georg; Lehmann, Laurent

2015-10-07

Many models proposed to study the evolution of collective action rely on a formalism that represents social interactions as n-player games between individuals adopting discrete actions such as cooperate and defect. Despite the importance of spatial structure in biological collective action, the analysis of n-player games games in spatially structured populations has so far proved elusive. We address this problem by considering mixed strategies and by integrating discrete-action n-player games into the direct fitness approach of social evolution theory. This allows to conveniently identify convergence stable strategies and to capture the effect of population structure by a single structure coefficient, namely, the pairwise (scaled) relatedness among interacting individuals. As an application, we use our mathematical framework to investigate collective action problems associated with the provision of three different kinds of collective goods, paradigmatic of a vast array of helping traits in nature: "public goods" (both providers and shirkers can use the good, e.g., alarm calls), "club goods" (only providers can use the good, e.g., participation in collective hunting), and "charity goods" (only shirkers can use the good, e.g., altruistic sacrifice). We show that relatedness promotes the evolution of collective action in different ways depending on the kind of collective good and its economies of scale. Our findings highlight the importance of explicitly accounting for relatedness, the kind of collective good, and the economies of scale in theoretical and empirical studies of the evolution of collective action. Copyright © 2015 Elsevier Ltd. All rights reserved.

Enhanced Old-New Recognition and Source Memory for Faces of Cooperators and Defectors in a Social-Dilemma Game

ERIC Educational Resources Information Center

Bell, Raoul; Buchner, Axel; Musch, Jochen

2010-01-01

A popular assumption in evolutionary psychology is that the human mind comprises specialized cognitive modules for social exchange, including a module that serves to enhance memory for faces of cheaters. In the present study, participants played a trust game with computerized opponents, who either defected or cooperated. In a control condition, no…

Evolutionary game theory meets social science: is there a unifying rule for human cooperation?

PubMed

Rosas, Alejandro

2010-05-21

Evolutionary game theory has shown that human cooperation thrives in different types of social interactions with a PD structure. Models treat the cooperative strategies within the different frameworks as discrete entities and sometimes even as contenders. Whereas strong reciprocity was acclaimed as superior to classic reciprocity for its ability to defeat defectors in public goods games, recent experiments and simulations show that costly punishment fails to promote cooperation in the IR and DR games, where classic reciprocity succeeds. My aim is to show that cooperative strategies across frameworks are capable of a unified treatment, for they are governed by a common underlying rule or norm. An analysis of the reputation and action rules that govern some representative cooperative strategies both in models and in economic experiments confirms that the different frameworks share a conditional action rule and several reputation rules. The common conditional rule contains an option between costly punishment and withholding benefits that provides alternative enforcement methods against defectors. Depending on the framework, individuals can switch to the appropriate strategy and method of enforcement. The stability of human cooperation looks more promising if one mechanism controls successful strategies across frameworks. Published by Elsevier Ltd.

Resistance to extreme strategies, rather than prosocial preferences, can explain human cooperation in public goods games.

PubMed

Kümmerli, Rolf; Burton-Chellew, Maxwell N; Ross-Gillespie, Adin; West, Stuart A

2010-06-01

The results of numerous economic games suggest that humans behave more cooperatively than would be expected if they were maximizing selfish interests. It has been argued that this is because individuals gain satisfaction from the success of others, and that such prosocial preferences require a novel evolutionary explanation. However, in previous games, imperfect behavior would automatically lead to an increase in cooperation, making it impossible to decouple any form of mistake or error from prosocial cooperative decisions. Here we empirically test between these alternatives by decoupling imperfect behavior from prosocial preferences in modified versions of the public goods game, in which individuals would maximize their selfish gain by completely (100%) cooperating. We found that, although this led to higher levels of cooperation, it did not lead to full cooperation, and individuals still perceived their group mates as competitors. This is inconsistent with either selfish or prosocial preferences, suggesting that the most parsimonious explanation is imperfect behavior triggered by psychological drives that can prevent both complete defection and complete cooperation. More generally, our results illustrate the caution that must be exercised when interpreting the evolutionary implications of economic experiments, especially the absolute level of cooperation in a particular treatment.

Evolutionary prisoner's dilemma games on the network with punishment and opportunistic partner switching

NASA Astrophysics Data System (ADS)

Takesue, H.

2018-02-01

Punishment and partner switching are two well-studied mechanisms that support the evolution of cooperation. Observation of human behaviour suggests that the extent to which punishment is adopted depends on the usage of alternative mechanisms, including partner switching. In this study, we investigate the combined effect of punishment and partner switching in evolutionary prisoner's dilemma games conducted on a network. In the model, agents are located on the network and participate in the prisoner's dilemma games with punishment. In addition, they can opportunistically switch interaction partners to improve their payoff. Our Monte Carlo simulation showed that a large frequency of punishers is required to suppress defectors when the frequency of partner switching is low. In contrast, cooperation is the most abundant strategy when the frequency of partner switching is high regardless of the strength of punishment. Interestingly, cooperators become abundant not because they avoid the cost of inflicting punishment and earn a larger average payoff per game but rather because they have more numerous opportunities to be referred to as a role agent by defectors. Our results imply that the fluidity of social relationships has a profound effect on the adopted strategy in maintaining cooperation.

Dynamic Gaming Platform (DGP)

DTIC Science & Technology

2009-04-01

GAMING PLATFORM (DGP) Lockheed Martin Corporation...YYYY) APR 09 2. REPORT TYPE Final 3. DATES COVERED (From - To) Jul 07 – Mar 09 4. TITLE AND SUBTITLE DYNAMIC GAMING PLATFORM (DGP) 5a...CMU Carnegie Mellon University DGP Dynamic Gaming Platform GA Genetic Algorithm IARPA Intelligence Advanced Research Projects Activity LM ATL Lockheed Martin Advanced Technology Laboratories PAINT ProActive INTelligence

Spectacular phenomena and limits to rationality in genetic and cultural evolution.

PubMed Central

Enquist, Magnus; Arak, Anthony; Ghirlanda, Stefano; Wachtmeister, Carl-Adam

2002-01-01

In studies of both animal and human behaviour, game theory is used as a tool for understanding strategies that appear in interactions between individuals. Game theory focuses on adaptive behaviour, which can be attained only at evolutionary equilibrium. We suggest that behaviour appearing during interactions is often outside the scope of such analysis. In many types of interaction, conflicts of interest exist between players, fuelling the evolution of manipulative strategies. Such strategies evolve out of equilibrium, commonly appearing as spectacular morphology or behaviour with obscure meaning, to which other players may react in non-adaptive, irrational ways. We present a simple model to show some limitations of the game-theory approach, and outline the conditions in which evolutionary equilibria cannot be maintained. Evidence from studies of biological interactions seems to support the view that behaviour is often not at equilibrium. This also appears to be the case for many human cultural traits, which have spread rapidly despite the fact that they have a negative influence on reproduction. PMID:12495515

Spectacular phenomena and limits to rationality in genetic and cultural evolution.

PubMed

Enquist, Magnus; Arak, Anthony; Ghirlanda, Stefano; Wachtmeister, Carl-Adam

2002-11-29

In studies of both animal and human behaviour, game theory is used as a tool for understanding strategies that appear in interactions between individuals. Game theory focuses on adaptive behaviour, which can be attained only at evolutionary equilibrium. We suggest that behaviour appearing during interactions is often outside the scope of such analysis. In many types of interaction, conflicts of interest exist between players, fuelling the evolution of manipulative strategies. Such strategies evolve out of equilibrium, commonly appearing as spectacular morphology or behaviour with obscure meaning, to which other players may react in non-adaptive, irrational ways. We present a simple model to show some limitations of the game-theory approach, and outline the conditions in which evolutionary equilibria cannot be maintained. Evidence from studies of biological interactions seems to support the view that behaviour is often not at equilibrium. This also appears to be the case for many human cultural traits, which have spread rapidly despite the fact that they have a negative influence on reproduction.

Chemical evolutionary games.

PubMed

Aristotelous, Andreas C; Durrett, Richard

2014-05-01

Inspired by the use of hybrid cellular automata in modeling cancer, we introduce a generalization of evolutionary games in which cells produce and absorb chemicals, and the chemical concentrations dictate the death rates of cells and their fitnesses. Our long term aim is to understand how the details of the interactions in a system with n species and m chemicals translate into the qualitative behavior of the system. Here, we study two simple 2×2 games with two chemicals and revisit the two and three species versions of the one chemical colicin system studied earlier by Durrett and Levin (1997). We find that in the 2×2 examples, the behavior of our new spatial model can be predicted from that of the mean field differential equation using ideas of Durrett and Levin (1994). However, in the three species colicin model, the system with diffusion does not have the coexistence which occurs in the lattices model in which sites interact with only their nearest neighbors. Copyright © 2014 Elsevier Inc. All rights reserved.

The influence of tie strength on evolutionary games on networks: An empirical investigation

NASA Astrophysics Data System (ADS)

Buesser, Pierre; Peña, Jorge; Pestelacci, Enea; Tomassini, Marco

2011-11-01

Extending previous work on unweighted networks, we present here a systematic numerical investigation of standard evolutionary games on weighted networks. In the absence of any reliable model for generating weighted social networks, we attribute weights to links in a few ways supported by empirical data ranging from totally uncorrelated to weighted bipartite networks. The results of the extensive simulation work on standard complex network models show that, except in a case that does not seem to be common in social networks, taking the tie strength into account does not change in a radical manner the long-run steady-state behavior of the studied games. Besides model networks, we also included a real-life case drawn from a coauthorship network. In this case also, taking the weights into account only changes the results slightly with respect to the raw unweighted graph, although to draw more reliable conclusions on real social networks many more cases should be studied as these weighted networks become available.

Deciphering the Counterplay of Aspergillus fumigatus Infection and Host Inflammation by Evolutionary Games on Graphs

NASA Astrophysics Data System (ADS)

Pollmächer, Johannes; Timme, Sandra; Schuster, Stefan; Brakhage, Axel A.; Zipfel, Peter F.; Figge, Marc Thilo

2016-06-01

Microbial invaders are ubiquitously present and pose the constant risk of infections that are opposed by various defence mechanisms of the human immune system. A tight regulation of the immune response ensures clearance of microbial invaders and concomitantly limits host damage that is crucial for host viability. To investigate the counterplay of infection and inflammation, we simulated the invasion of the human-pathogenic fungus Aspergillus fumigatus in lung alveoli by evolutionary games on graphs. The layered structure of the innate immune system is represented by a sequence of games in the virtual model. We show that the inflammatory cascade of the immune response is essential for microbial clearance and that the inflammation level correlates with the infection-dose. At low infection-doses, corresponding to daily inhalation of conidia, the resident alveolar macrophages may be sufficient to clear infections, however, at higher infection-doses their primary task shifts towards recruitment of neutrophils to infection sites.

Deciphering the Counterplay of Aspergillus fumigatus Infection and Host Inflammation by Evolutionary Games on Graphs

PubMed Central

Pollmächer, Johannes; Timme, Sandra; Schuster, Stefan; Brakhage, Axel A.; Zipfel, Peter F.; Figge, Marc Thilo

2016-01-01

Microbial invaders are ubiquitously present and pose the constant risk of infections that are opposed by various defence mechanisms of the human immune system. A tight regulation of the immune response ensures clearance of microbial invaders and concomitantly limits host damage that is crucial for host viability. To investigate the counterplay of infection and inflammation, we simulated the invasion of the human-pathogenic fungus Aspergillus fumigatus in lung alveoli by evolutionary games on graphs. The layered structure of the innate immune system is represented by a sequence of games in the virtual model. We show that the inflammatory cascade of the immune response is essential for microbial clearance and that the inflammation level correlates with the infection-dose. At low infection-doses, corresponding to daily inhalation of conidia, the resident alveolar macrophages may be sufficient to clear infections, however, at higher infection-doses their primary task shifts towards recruitment of neutrophils to infection sites. PMID:27291424

Genome-driven evolutionary game theory helps understand the rise of metabolic interdependencies in microbial communities.

PubMed

Zomorrodi, Ali R; Segrè, Daniel

2017-11-16

Metabolite exchanges in microbial communities give rise to ecological interactions that govern ecosystem diversity and stability. It is unclear, however, how the rise of these interactions varies across metabolites and organisms. Here we address this question by integrating genome-scale models of metabolism with evolutionary game theory. Specifically, we use microbial fitness values estimated by metabolic models to infer evolutionarily stable interactions in multi-species microbial "games". We first validate our approach using a well-characterized yeast cheater-cooperator system. We next perform over 80,000 in silico experiments to infer how metabolic interdependencies mediated by amino acid leakage in Escherichia coli vary across 189 amino acid pairs. While most pairs display shared patterns of inter-species interactions, multiple deviations are caused by pleiotropy and epistasis in metabolism. Furthermore, simulated invasion experiments reveal possible paths to obligate cross-feeding. Our study provides genomically driven insight into the rise of ecological interactions, with implications for microbiome research and synthetic ecology.

Economic Game Theory to Model the Attenuation of Virulence of an Obligate Intracellular Bacterium.

PubMed

Tago, Damian; Meyer, Damien F

2016-01-01

Diseases induced by obligate intracellular pathogens have a large burden on global human and animal health. Understanding the factors involved in the virulence and fitness of these pathogens contributes to the development of control strategies against these diseases. Based on biological observations, a theoretical model using game theory is proposed to explain how obligate intracellular bacteria interact with their host. The equilibrium in such a game shows that the virulence and fitness of the bacterium is host-triggered and by changing the host's defense system to which the bacterium is confronted, an evolutionary process leads to an attenuated strain. Although, the attenuation procedure has already been conducted in practice in order to develop an attenuated vaccine (e.g., with Ehrlichia ruminantium), there was a lack of understanding of the theoretical basis behind this process. Our work provides a model to better comprehend the existence of different phenotypes and some underlying evolutionary mechanisms for the virulence of obligate intracellular bacteria.

Economic Game Theory to Model the Attenuation of Virulence of an Obligate Intracellular Bacterium

PubMed Central

Tago, Damian; Meyer, Damien F.

2016-01-01

Diseases induced by obligate intracellular pathogens have a large burden on global human and animal health. Understanding the factors involved in the virulence and fitness of these pathogens contributes to the development of control strategies against these diseases. Based on biological observations, a theoretical model using game theory is proposed to explain how obligate intracellular bacteria interact with their host. The equilibrium in such a game shows that the virulence and fitness of the bacterium is host-triggered and by changing the host's defense system to which the bacterium is confronted, an evolutionary process leads to an attenuated strain. Although, the attenuation procedure has already been conducted in practice in order to develop an attenuated vaccine (e.g., with Ehrlichia ruminantium), there was a lack of understanding of the theoretical basis behind this process. Our work provides a model to better comprehend the existence of different phenotypes and some underlying evolutionary mechanisms for the virulence of obligate intracellular bacteria. PMID:27610355

Altruistic behavior pays, or the importance of fluctuations in evolutionary game theory

NASA Astrophysics Data System (ADS)

Sánchez, Angel; Cuesta, José A.; Roca, Carlos P.

2005-07-01

Human behavior is one of the main problems for evolution, as it is often the case that human actions are disadvantageous for the self and advantageous for other people. Behind this puzzle are our beliefs about rational behavior, based on game theory. Here we show that by going beyond the standard game-theoretical conventions, apparently altruistic behavior can be understood as self-interested. We discuss in detail an example related to the so called Ultimatum game and illustrate the appearance of altruistic behavior induced by fluctuations. In addition, we claim that in general settings, fluctuations play a very relevant role, and we support this claim by considering a completely different example, namely the Stag-Hunt game.

Coevolutionary dynamics in large, but finite populations

NASA Astrophysics Data System (ADS)

Traulsen, Arne; Claussen, Jens Christian; Hauert, Christoph

2006-07-01

Coevolving and competing species or game-theoretic strategies exhibit rich and complex dynamics for which a general theoretical framework based on finite populations is still lacking. Recently, an explicit mean-field description in the form of a Fokker-Planck equation was derived for frequency-dependent selection with two strategies in finite populations based on microscopic processes [A. Traulsen, J. C. Claussen, and C. Hauert, Phys. Rev. Lett. 95, 238701 (2005)]. Here we generalize this approach in a twofold way: First, we extend the framework to an arbitrary number of strategies and second, we allow for mutations in the evolutionary process. The deterministic limit of infinite population size of the frequency-dependent Moran process yields the adjusted replicator-mutator equation, which describes the combined effect of selection and mutation. For finite populations, we provide an extension taking random drift into account. In the limit of neutral selection, i.e., whenever the process is determined by random drift and mutations, the stationary strategy distribution is derived. This distribution forms the background for the coevolutionary process. In particular, a critical mutation rate uc is obtained separating two scenarios: above uc the population predominantly consists of a mixture of strategies whereas below uc the population tends to be in homogeneous states. For one of the fundamental problems in evolutionary biology, the evolution of cooperation under Darwinian selection, we demonstrate that the analytical framework provides excellent approximations to individual based simulations even for rather small population sizes. This approach complements simulation results and provides a deeper, systematic understanding of coevolutionary dynamics.

Competition among cooperators: Altruism and reciprocity

PubMed Central

Danielson, Peter

2002-01-01

Levine argues that neither self-interest nor altruism explains experimental results in bargaining and public goods games. Subjects' preferences appear also to be sensitive to their opponents' perceived altruism. Sethi and Somanathan provide a general account of reciprocal preferences that survive under evolutionary pressure. Although a wide variety of reciprocal strategies pass this evolutionary test, Sethi and Somanthan conjecture that fewer are likely to survive when reciprocal strategies compete with each other. This paper develops evolutionary agent-based models to test their conjecture in cases where reciprocal preferences can differ in a variety of games. We confirm that reciprocity is necessary but not sufficient for optimal cooperation. We explore the theme of competition among reciprocal cooperators and display three interesting emergent organizations: racing to the “moral high ground,” unstable cycles of preference change, and, when we implement reciprocal mechanisms, hierarchies resulting from exploiting fellow cooperators. If reciprocity is a basic mechanism facilitating cooperation, we can expect interaction that evolves around it to be complex, non-optimal, and resistant to change. PMID:12011403

Diversity of neighborhoods promotes cooperation in evolutionary social dilemmas

NASA Astrophysics Data System (ADS)

Ma, Yongjuan; Lu, Jun; Shi, Lei

2017-02-01

Explaining the evolution of cooperative behavior is one of the most important and interesting problems in a myriad of disciplines, such as evolutionary biology, mathematics, statistical physics, social science and economics Up to now, there have been a great number of works aiming to this issue with the help of evolutionary game theory. However, vast majority of existing literatures simply assume that the interaction neighborhood and replacement neighborhood are symmetric, which seems inconsistent with real-world cases. In this paper, we consider the asymmetrical neighborhood: player of type A, whose factor is controlled by a parameter τ, has four interaction neighbors and four replacement neighbors, while player of type B, whose factor is controlled by a parameter 1 - τ, possess eight interaction neighbors and four replacement neighbors. By means of numerous Monte Carlo simulations, we found that middle τ can make the cooperation reach the highest level While for this finding, its robustness can be further validated in more games.

The promotion of cooperation by the poor in dynamic chicken games

NASA Astrophysics Data System (ADS)

Ito, Hiromu; Katsumata, Yuki; Hasegawa, Eisuke; Yoshimura, Jin

2017-02-01

The evolution of cooperative behavior is one of the most important issues in game theory. Previous studies have shown that cooperation can evolve only under highly limited conditions, and various modifications have been introduced to games to explain the evolution of cooperation. Recently, a utility function basic to game theory was shown to be dependent on current wealth as a conditional (state) variable in a dynamic version of utility theory. Here, we introduce this dynamic utility function to several games. Under certain conditions, poor players exhibit cooperative behavior in two types of chicken games (the hawk-dove game and the snowdrift game) but not in the prisoner’s dilemma game and the stag hunt game. This result indicates that cooperation can be exhibited by the poor in some chicken games. Thus, the evolution of cooperation may not be as limited as has been suggested in previous studies.

Game Theory Paradigm: A New Tool for Investigating Social Dysfunction in Major Depressive Disorders

PubMed Central

Wang, Yun; Yang, Liu-Qing; Li, Shu; Zhou, Yuan

2015-01-01

Social dysfunction is a prominent source of distress and disability in patients with major depressive disorder (MDD) but is commonly omitted from current clinical studies, although some researchers propose an evolutionary strategy to understand these negative outcomes. Limited knowledge about the neural basis of social dysfunction in MDD results from traditional paradigms, which lack insights into social interactions. Game theoretical modeling offers a new tool for investigating social-interaction impairments in neuropsychiatric disorders. This review first introduces three widely used games from game theory and the major behavioral and neuroimaging findings obtained using these games in healthy populations. We also address the factors that modulate behaviors in games and their neural bases. We then summarize the current findings obtained by using these games in depressed patients and discuss the clinical implications of these abnormal game behaviors. Finally, we briefly discuss future prospects that may further elucidate the clinical use of a game theory paradigm in MDD. PMID:26441689

Game Theory Paradigm: A New Tool for Investigating Social Dysfunction in Major Depressive Disorders.

PubMed

Wang, Yun; Yang, Liu-Qing; Li, Shu; Zhou, Yuan

2015-01-01

Social dysfunction is a prominent source of distress and disability in patients with major depressive disorder (MDD) but is commonly omitted from current clinical studies, although some researchers propose an evolutionary strategy to understand these negative outcomes. Limited knowledge about the neural basis of social dysfunction in MDD results from traditional paradigms, which lack insights into social interactions. Game theoretical modeling offers a new tool for investigating social-interaction impairments in neuropsychiatric disorders. This review first introduces three widely used games from game theory and the major behavioral and neuroimaging findings obtained using these games in healthy populations. We also address the factors that modulate behaviors in games and their neural bases. We then summarize the current findings obtained by using these games in depressed patients and discuss the clinical implications of these abnormal game behaviors. Finally, we briefly discuss future prospects that may further elucidate the clinical use of a game theory paradigm in MDD.

Investigation on Law and Economics Based on Complex Network and Time Series Analysis

PubMed Central

Yang, Jian; Qu, Zhao; Chang, Hui

2015-01-01

The research focuses on the cooperative relationship and the strategy tendency among three mutually interactive parties in financing: small enterprises, commercial banks and micro-credit companies. Complex network theory and time series analysis were applied to figure out the quantitative evidence. Moreover, this paper built up a fundamental model describing the particular interaction among them through evolutionary game. Combining the results of data analysis and current situation, it is justifiable to put forward reasonable legislative recommendations for regulations on lending activities among small enterprises, commercial banks and micro-credit companies. The approach in this research provides a framework for constructing mathematical models and applying econometrics and evolutionary game in the issue of corporation financing. PMID:26076460

Effects of Inertia on Evolutionary Prisoner's Dilemma Game

NASA Astrophysics Data System (ADS)

Du, Wen-Bo; Cao, Xian-Bin; Liu, Run-Ran; Wang, Zhen

2012-09-01

Considering the inertia of individuals in real life, we propose a modified Fermi updating rule, where the inertia of players is introduced into evolutionary prisoner's dilemma game (PDG) on square lattices. We mainly focus on how the inertia affects the cooperative behavior of the system. Interestingly, we find that the cooperation level has a nonmonotonic dependence on the inertia: with small inertia, cooperators will soon be invaded by defectors; with large inertia, players are unwilling to change their strategies and the cooperation level remains the same as the initial state; while a moderate inertia can induce the highest cooperation level. Moreover, effects of environmental noise and individual inertia are studied. Our work may be helpful in understanding the emergence and persistence of cooperation in nature and society.

Communication scheme based on evolutionary spatial 2×2 games

NASA Astrophysics Data System (ADS)

Ziaukas, Pranas; Ragulskis, Tautvydas; Ragulskis, Minvydas

2014-06-01

A visual communication scheme based on evolutionary spatial 2×2 games is proposed in this paper. Self-organizing patterns induced by complex interactions between competing individuals are exploited for hiding and transmitting secret visual information. Properties of the proposed communication scheme are discussed in details. It is shown that the hiding capacity of the system (the minimum size of the detectable primitives and the minimum distance between two primitives) is sufficient for the effective transmission of digital dichotomous images. Also, it is demonstrated that the proposed communication scheme is resilient to time backwards, plain image attacks and is highly sensitive to perturbations of private and public keys. Several computational experiments are used to demonstrate the effectiveness of the proposed communication scheme.

Memory does not necessarily promote cooperation in dilemma games

NASA Astrophysics Data System (ADS)

Wang, Tao; Chen, Zhigang; Li, Kenli; Deng, Xiaoheng; Li, Deng

2014-02-01

Evolutionary games can model dilemmas for which cooperation can exist in rational populations. According to intuition, memory of the history can help individuals to overcome the dilemma and increase cooperation. However, here we show that no such general predictions can be made for dilemma games with memory. Agents play repeated prisoner’s dilemma, snowdrift, or stag hunt games in well-mixed populations or on a lattice. We compare the cooperation ratio and fitness for systems with or without memory. An interesting result is that cooperation is demoted in snowdrift and stag hunt games with memory when cost-to-benefit ratio is low, while system fitness still increases with memory in the snowdrift game. To illustrate this interesting phenomenon, two further experiments were performed to study R, ST, and P reciprocity and investigate 16 agent strategies for one-step memory. The results show that memory plays different roles in different dilemma games.

Argoball: A Dynamic-Rules Game for Teaching Striking-and-Fielding Game Tactics

ERIC Educational Resources Information Center

Todorovich, John R.; Fox, James P.; Ryan, Stuart; Todorovich, Sarah W.

2008-01-01

Physical educators using the teaching games for understanding (TGFU) approach employ modified game forms to teach children skills and tactics. Inspired by Danish Longball, "Argoball" is a dynamic-rules game that teachers interested in the TGFU model use to help their students develop effective skills and tactics to better participate in…

Gaming Personality and Game Dynamics in Online Discussion Instructions

ERIC Educational Resources Information Center

Tu, Chih-Hsiung; Yen, Cherng-Jyh; Sujo-Montes, Laura; Roberts, Gayle A.

2015-01-01

Gamification is the use of game mechanics to drive game-like engagements and actions. It applies game mechanics, dynamics and frameworks to promote desired learning behaviours. Positive and effective gamification could enhance learning and engage learners in more social and context-rich decision-making for problem-solving in learning tasks.…

Multilevel selection in a resource-based model.

PubMed

Ferreira, Fernando Fagundes; Campos, Paulo R A

2013-07-01

In the present work we investigate the emergence of cooperation in a multilevel selection model that assumes limiting resources. Following the work by R. J. Requejo and J. Camacho [Phys. Rev. Lett. 108, 038701 (2012)], the interaction among individuals is initially ruled by a prisoner's dilemma (PD) game. The payoff matrix may change, influenced by the resource availability, and hence may also evolve to a non-PD game. Furthermore, one assumes that the population is divided into groups, whose local dynamics is driven by the payoff matrix, whereas an intergroup competition results from the nonuniformity of the growth rate of groups. We study the probability that a single cooperator can invade and establish in a population initially dominated by defectors. Cooperation is strongly favored when group sizes are small. We observe the existence of a critical group size beyond which cooperation becomes counterselected. Although the critical size depends on the parameters of the model, it is seen that a saturation value for the critical group size is achieved. The results conform to the thought that the evolutionary history of life repeatedly involved transitions from smaller selective units to larger selective units.

The evolution of prompt reaction to adverse ties

PubMed Central

2008-01-01

Background In recent years it has been found that the combination of evolutionary game theory with population structures modelled in terms of dynamical graphs, in which individuals are allowed to sever unwanted social ties while keeping the good ones, provides a viable solution to the conundrum of cooperation. It is well known that in reality individuals respond differently to disadvantageous interactions. Yet, the evolutionary mechanism determining the individuals' willingness to sever unfavourable ties remains unclear. Results We introduce a novel way of thinking about the joint evolution of cooperation and social contacts. The struggle for survival between cooperators and defectors leads to an arms race for swiftness in adjusting social ties, based purely on a self-regarding, individual judgement. Since defectors are never able to establish social ties under mutual agreement, they break adverse ties more rapidly than cooperators, who tend to evolve stable and long-term relations. Ironically, defectors' constant search for partners to exploit leads to heterogeneous networks that improve the survivability of cooperators, compared to the traditional homogenous population assumption. Conclusion When communities face the prisoner's dilemma, swift reaction to adverse ties evolves when competition is fierce between cooperators and defectors, providing an evolutionary basis for the necessity of individuals to adjust their social ties. Our results show how our innate resilience to change relates to mutual agreement between cooperators and how "loyalty" or persistent social ties bring along an evolutionary disadvantage, both from an individual and group perspective. PMID:18928551

Eco-evolutionary feedbacks, adaptive dynamics and evolutionary rescue theory

PubMed Central

Ferriere, Regis; Legendre, Stéphane

2013-01-01

Adaptive dynamics theory has been devised to account for feedbacks between ecological and evolutionary processes. Doing so opens new dimensions to and raises new challenges about evolutionary rescue. Adaptive dynamics theory predicts that successive trait substitutions driven by eco-evolutionary feedbacks can gradually erode population size or growth rate, thus potentially raising the extinction risk. Even a single trait substitution can suffice to degrade population viability drastically at once and cause ‘evolutionary suicide’. In a changing environment, a population may track a viable evolutionary attractor that leads to evolutionary suicide, a phenomenon called ‘evolutionary trapping’. Evolutionary trapping and suicide are commonly observed in adaptive dynamics models in which the smooth variation of traits causes catastrophic changes in ecological state. In the face of trapping and suicide, evolutionary rescue requires that the population overcome evolutionary threats generated by the adaptive process itself. Evolutionary repellors play an important role in determining how variation in environmental conditions correlates with the occurrence of evolutionary trapping and suicide, and what evolutionary pathways rescue may follow. In contrast with standard predictions of evolutionary rescue theory, low genetic variation may attenuate the threat of evolutionary suicide and small population sizes may facilitate escape from evolutionary traps. PMID:23209163

Preschool Children Fail Primate Prosocial Game Because of Attentional Task Demands

PubMed Central

Burkart, Judith Maria; Rueth, Katja

2013-01-01

Various nonhuman primate species have been tested with prosocial games (i.e. derivates from dictator games) in order to better understand the evolutionary origin of proactive prosociality in humans. Results of these efforts are mixed, and it is difficult to disentangle true species differences from methodological artifacts. We tested 2- to 5-year-old children with a costly and a cost-free version of a prosocial game that differ with regard to the payoff distribution and are widely used with nonhuman primates. Simultaneously, we assessed the subjects’ level of Theory of Mind understanding. Prosocial behavior was demonstrated with the prosocial game, and did not increase with more advanced Theory of Mind understanding. However, prosocial behavior could only be detected with the costly version of the game, whereas the children failed the cost-free version that is most commonly used with nonhuman primates. A detailed comparison of the children’s behavior in the two versions of the game indicates that the failure was due to higher attentional demands of the cost-free version, rather than to a lack of prosociality per se. Our results thus show (i) that subtle differences in prosociality tasks can substantially bias the outcome and thus prevent meaningful species comparisons, and (ii) that like in nonhuman primates, prosocial behavior in human children does not require advanced Theory of Mind understanding in the present context. However, both developmental and comparative psychology accumulate increasing evidence for the multidimensionality of prosocial behaviors, suggesting that different forms of prosociality are also regulated differentially. For future efforts to understand the evolutionary origin of prosociality it is thus crucial to take this heterogeneity into account. PMID:23844201

Preschool children fail primate prosocial game because of attentional task demands.

PubMed

Burkart, Judith Maria; Rueth, Katja

2013-01-01

Various nonhuman primate species have been tested with prosocial games (i.e. derivates from dictator games) in order to better understand the evolutionary origin of proactive prosociality in humans. Results of these efforts are mixed, and it is difficult to disentangle true species differences from methodological artifacts. We tested 2- to 5-year-old children with a costly and a cost-free version of a prosocial game that differ with regard to the payoff distribution and are widely used with nonhuman primates. Simultaneously, we assessed the subjects' level of Theory of Mind understanding. Prosocial behavior was demonstrated with the prosocial game, and did not increase with more advanced Theory of Mind understanding. However, prosocial behavior could only be detected with the costly version of the game, whereas the children failed the cost-free version that is most commonly used with nonhuman primates. A detailed comparison of the children's behavior in the two versions of the game indicates that the failure was due to higher attentional demands of the cost-free version, rather than to a lack of prosociality per se. Our results thus show (i) that subtle differences in prosociality tasks can substantially bias the outcome and thus prevent meaningful species comparisons, and (ii) that like in nonhuman primates, prosocial behavior in human children does not require advanced Theory of Mind understanding in the present context. However, both developmental and comparative psychology accumulate increasing evidence for the multidimensionality of prosocial behaviors, suggesting that different forms of prosociality are also regulated differentially. For future efforts to understand the evolutionary origin of prosociality it is thus crucial to take this heterogeneity into account.

Heterogeneity and proliferation of invasive cancer subclones in game theory models of the Warburg effect.

PubMed

Archetti, M

2015-04-01

The Warburg effect, a switch from aerobic energy production to anaerobic glycolysis, promotes tumour proliferation and motility by inducing acidification of the tumour microenvironment. Therapies that reduce acidity could impair tumour growth and invasiveness. I analysed the dynamics of cell proliferation and of resistance to therapies that target acidity, in a population of cells, under the Warburg effect. The dynamics of mutant cells with increased glycolysis and motility has been assessed in a multi-player game with collective interactions in the framework of evolutionary game theory. Perturbations of the level of acidity in the microenvironment have been used to simulate the effect of therapies that target glycolysis. The non-linear effects of glycolysis induce frequency-dependent clonal selection leading to coexistence of glycolytic and non-glycolytic cells within a tumour. Mutants with increased motility can invade such a polymorphic population and spread within the tumour. While reducing acidity may produce a sudden reduction in tumour cell proliferation, frequency-dependent selection enables it to adapt to the new conditions and can enable the tumour to restore its original levels of growth and invasiveness. The acidity produced by glycolysis acts as a non-linear public good that leads to coexistence of cells with high and low glycolysis within the tumour. Such a heterogeneous population can easily adapt to changes in acidity. Therapies that target acidity can only be effective in the long term if the cost of glycolysis is high, that is, under non-limiting oxygen concentrations. Their efficacy, therefore, is reduced when combined with therapies that impair angiogenesis. © 2015 The Authors Cell Proliferation Published by John Wiley & Sons Ltd.

State-Dependent Risk Preferences in Evolutionary Games

NASA Astrophysics Data System (ADS)

Roos, Patrick; Nau, Dana

There is much empirical evidence that human decision-making under risk does not correspond the decision-theoretic notion of "rational" decision making, namely to make choices that maximize the expected value. An open question is how such behavior could have arisen evolutionarily. We believe that the answer to this question lies, at least in part, in the interplay between risk-taking and sequentiality of choice in evolutionary environments.

Algorithm for Overcoming the Curse of Dimensionality for Certain Non-convex Hamilton-Jacobi Equations, Projections and Differential Games

DTIC Science & Technology

2016-05-01

Algorithm for Overcoming the Curse of Dimensionality for Certain Non-convex Hamilton-Jacobi Equations, Projections and Differential Games Yat Tin...subproblems. Our approach is expected to have wide applications in continuous dynamic games , control theory problems, and elsewhere. Mathematics...differential dynamic games , control theory problems, and dynamical systems coming from the physical world, e.g. [11]. An important application is to

A Game-Theory Based Incentive Framework for an Intelligent Traffic System as Part of a Smart City Initiative

PubMed Central

Mei, Haibo; Poslad, Stefan; Du, Shuang

2017-01-01

Intelligent Transportation Systems (ITSs) can be applied to inform and incentivize travellers to help them make cognizant choices concerning their trip routes and transport modality use for their daily travel whilst achieving more sustainable societal and transport authority goals. However, in practice, it is challenging for an ITS to enable incentive generation that is context-driven and personalized, whilst supporting multi-dimensional travel goals. This is because an ITS has to address the situation where different travellers have different travel preferences and constraints for route and modality, in the face of dynamically-varying traffic conditions. Furthermore, personalized incentive generation also needs to dynamically achieve different travel goals from multiple travellers, in the face of their conducts being a mix of both competitive and cooperative behaviours. To address this challenge, a Rule-based Incentive Framework (RIF) is proposed in this paper that utilizes both decision tree and evolutionary game theory to process travel information and intelligently generate personalized incentives for travellers. The travel information processed includes travellers’ mobile patterns, travellers’ modality preferences and route traffic volume information. A series of MATLAB simulations of RIF was undertaken to validate RIF to show that it is potentially an effective way to incentivize travellers to change travel routes and modalities as an essential smart city service. PMID:29232907

Player guild dynamics and evolution in massively multiplayer online games.

PubMed

Chen, Chien-Hsun; Sun, Chuen-Tsai; Hsieh, Jilung

2008-06-01

In the latest versions of massively multiplayer online games (MMOGs), developers have purposefully made guilds part of game environments. Guilds represent a powerful method for giving players a sense of online community, but there is little quantitative data on guild dynamics. To address this topic, we took advantage of a feature found in one of today's most popular MMOGs (World of Warcraft) to collect in-game data: user interfaces that players can modify and refine. In addition to collecting data on in-game player activities, we used this feature to observe and investigate how players join and leave guilds. Data were analyzed for the purpose of identifying factors that propel game-world guild dynamics and evolution. After collecting data for 641,805 avatars on 62 Taiwanese World of Warcraft game servers between February 10 and April 10, 2006, we created five guild type categories (small, large, elite, newbie, and unstable) that have different meanings in terms of in-game group dynamics. By viewing players as the most important resource affecting guild life cycles, it is possible to analyze game worlds as ecosystems consisting of evolving guilds and to study how guild life cycles reflect game world characteristics.

Spatio-temporal dynamics of security investments in an interdependent risk environment

NASA Astrophysics Data System (ADS)

Shafi, Kamran; Bender, Axel; Zhong, Weicai; Abbass, Hussein A.

2012-10-01

In a globalised world where risks spread through contagion, the decision of an entity to invest in securing its premises from stochastic risks no longer depends solely on its own actions but also on the actions of other interacting entities in the system. This phenomenon is commonly seen in many domains including airline, logistics and computer security and is referred to as Interdependent Security (IDS). An IDS game models this decision problem from a game-theoretic perspective and deals with the behavioural dynamics of risk-reduction investments in such settings. This paper enhances this model and investigates the spatio-temporal aspects of the IDS games. The spatio-temporal dynamics are studied using simple replicator dynamics on a variety of network structures and for various security cost tradeoffs that lead to different Nash equilibria in an IDS game. The simulation results show that the neighbourhood configuration has a greater effect on the IDS game dynamics than network structure. An in-depth empirical analysis of game dynamics is carried out on regular graphs, which leads to the articulation of necessary and sufficient conditions for dominance in IDS games under spatial constraints.

Social games in a social network.

PubMed

Abramson, G; Kuperman, M

2001-03-01

We study an evolutionary version of the Prisoner's Dilemma game, played by agents placed in a small-world network. Agents are able to change their strategy, imitating that of the most successful neighbor. We observe that different topologies, ranging from regular lattices to random graphs, produce a variety of emergent behaviors. This is a contribution towards the study of social phenomena and transitions governed by the topology of the community.

Goal-based dictator game

NASA Astrophysics Data System (ADS)

Zaibidi, Nerda Zura; Ibrahim, Adyda; Abidin, Norhaslinda Zainal

2014-12-01

A considerable number of studies have been conducted to study fairness issues using two-player game. Dictator Game is one of the two-player games that receive much attention. In this paper, we develop an evolutionary approach to the Dictator Game by using Goal programming to build a model of human decision-making for cooperation. The model is formulated based on the theories of cognitive neuroscience that is capable in capturing a more realistic fairness concerns between players in the games. We show that fairness will evolve by taking into account players' aspirations and preferences explicitly in terms of profit and fairness concerns. The model is then simulated to investigate any possible effective strategy for people in economics to deal with fairness coalition. Parallels are drawn between the approach and concepts of human decision making from the field of cognitive neuroscience and psychology. The proposed model is also able to help decision makers to plan or enhance the effective strategies for business purposes.

Selfishness, fraternity, and other-regarding preference in spatial evolutionary games.

PubMed

Szabó, György; Szolnoki, Attila

2012-04-21

Spatial evolutionary games are studied with myopic players whose payoff interest, as a personal character, is tuned from selfishness to other-regarding preference via fraternity. The players are located on a square lattice and collect income from symmetric two-person two-strategy (called cooperation and defection) games with their nearest neighbors. During the elementary steps of evolution a randomly chosen player modifies her strategy in order to maximize stochastically her utility function composed from her own and the co-players' income with weight factors 1-Q and Q. These models are studied within a wide range of payoff parameters using Monte Carlo simulations for noisy strategy updates and by spatial stability analysis in the low noise limit. For fraternal players (Q=1/2) the system evolves into ordered arrangements of strategies in the low noise limit in a way providing optimum payoff for the whole society. Dominance of defectors, representing the "tragedy of the commons", is found within the regions of prisoner's dilemma and stag hunt game for selfish players (Q=0). Due to the symmetry in the effective utility function the system exhibits similar behavior even for Q=1 that can be interpreted as the "lovers' dilemma". Copyright © 2011 Elsevier Ltd. All rights reserved.

Evolution of cooperation through adaptive interaction in a spatial prisoner's dilemma game

NASA Astrophysics Data System (ADS)

Pan, Qiuhui; Liu, Xuesong; Bao, Honglin; Su, Yu; He, Mingfeng

2018-02-01

In this paper, we study the effect of adaptive interaction on the evolution of cooperation in a spatial prisoner's dilemma game. The connections of players are co-evolutionary with cooperation; whether adjacent players can play the prisoner's dilemma game is associated with the strategies they took in the preceding round. If a player defected in the preceding round, his neighbors will refuse to play the prisoner's dilemma game with him in accordance with a certain probability distribution. We use the disconnecting strength to represent this probability. We discuss the evolution of cooperation with different values of temptation to defect, sucker's payoff and disconnecting strength. The simulation results show that cooperation can be significantly enhanced through increasing the value of the disconnecting strength. In addition, the increase in disconnecting strength can improve the cooperators' ability to resist the increase in temptation and the decrease in reward. We study the parameter ranges for three different evolutionary results: cooperators extinction, defectors extinction, cooperator and defector co-existence. Meanwhile, we recruited volunteers and designed a human behavioral experiment to verify the theoretical simulation results. The punishment of disconnection has a positive effect on cooperation. A higher disconnecting strength will enhance cooperation more significantly. Our research findings reveal some significant insights into efficient mechanisms of the evolution of cooperation.

Non-cooperative game theory in biology and cooperative reasoning in humans.

PubMed

Kabalak, Alihan; Smirnova, Elena; Jost, Jürgen

2015-06-01

The readiness for spontaneous cooperation together with the assumptions that others share this cooperativity has been identified as a fundamental feature that distinguishes humans from other animals, including the great apes. At the same time, cooperativity presents an evolutionary puzzle because non-cooperators do better in a group of cooperators. We develop here an analysis of the process leading to cooperation in terms of rationality concepts, game theory and epistemic logic. We are, however, not attempting to reconstruct the actual evolutionary process. We rather want to provide the logical structure underlying cooperation in order to understand why cooperation is possible and what kind of reasoning and beliefs would lead to cooperative decision-making. Game theory depends on an underlying common belief in non-cooperative rationality of the players, and cooperativity similarly can utilize a common belief in cooperative rationality as its basis. We suggest a weaker concept of rational decision-making in games that encompasses both types of decision-making. We build this up in stages, starting from simple optimization, then using anticipation of the reaction of others, to finally arrive at reflexive and cooperative reasoning. While each stage is more difficult than the preceding, importantly, we also identify a reduction of complexity achieved by the consistent application of higher stage reasoning.

Form of an evolutionary tradeoff affects eco-evolutionary dynamics in a predator-prey system.

PubMed

Kasada, Minoru; Yamamichi, Masato; Yoshida, Takehito

2014-11-11

Evolution on a time scale similar to ecological dynamics has been increasingly recognized for the last three decades. Selection mediated by ecological interactions can change heritable phenotypic variation (i.e., evolution), and evolution of traits, in turn, can affect ecological interactions. Hence, ecological and evolutionary dynamics can be tightly linked and important to predict future dynamics, but our understanding of eco-evolutionary dynamics is still in its infancy and there is a significant gap between theoretical predictions and empirical tests. Empirical studies have demonstrated that the presence of genetic variation can dramatically change ecological dynamics, whereas theoretical studies predict that eco-evolutionary dynamics depend on the details of the genetic variation, such as the form of a tradeoff among genotypes, which can be more important than the presence or absence of the genetic variation. Using a predator-prey (rotifer-algal) experimental system in laboratory microcosms, we studied how different forms of a tradeoff between prey defense and growth affect eco-evolutionary dynamics. Our experimental results show for the first time to our knowledge that different forms of the tradeoff produce remarkably divergent eco-evolutionary dynamics, including near fixation, near extinction, and coexistence of algal genotypes, with quantitatively different population dynamics. A mathematical model, parameterized from completely independent experiments, explains the observed dynamics. The results suggest that knowing the details of heritable trait variation and covariation within a population is essential for understanding how evolution and ecology will interact and what form of eco-evolutionary dynamics will result.

Evolutionary dynamics for persistent cooperation in structured populations

NASA Astrophysics Data System (ADS)

Li, Yan; Liu, Xinsheng; Claussen, Jens Christian; Guo, Wanlin

2015-06-01

The emergence and maintenance of cooperative behavior is a fascinating topic in evolutionary biology and social science. The public goods game (PGG) is a paradigm for exploring cooperative behavior. In PGG, the total resulting payoff is divided equally among all participants. This feature still leads to the dominance of defection without substantially magnifying the public good by a multiplying factor. Much effort has been made to explain the evolution of cooperative strategies, including a recent model in which only a portion of the total benefit is shared by all the players through introducing a new strategy named persistent cooperation. A persistent cooperator is a contributor who is willing to pay a second cost to retrieve the remaining portion of the payoff contributed by themselves. In a previous study, this model was analyzed in the framework of well-mixed populations. This paper focuses on discussing the persistent cooperation in lattice-structured populations. The evolutionary dynamics of the structured populations consisting of three types of competing players (pure cooperators, defectors, and persistent cooperators) are revealed by theoretical analysis and numerical simulations. In particular, the approximate expressions of fixation probabilities for strategies are derived on one-dimensional lattices. The phase diagrams of stationary states, and the evolution of frequencies and spatial patterns for strategies are illustrated on both one-dimensional and square lattices by simulations. Our results are consistent with the general observation that, at least in most situations, a structured population facilitates the evolution of cooperation. Specifically, here we find that the existence of persistent cooperators greatly suppresses the spreading of defectors under more relaxed conditions in structured populations compared to that obtained in well-mixed populations.

Evolution of fairness in the one-shot anonymous Ultimatum Game

PubMed Central

Rand, David G.; Tarnita, Corina E.; Ohtsuki, Hisashi; Nowak, Martin A.

2013-01-01

Classical economic models assume that people are fully rational and selfish, while experiments often point to different conclusions. A canonical example is the Ultimatum Game: one player proposes a division of a sum of money between herself and a second player, who either accepts or rejects. Based on rational self-interest, responders should accept any nonzero offer and proposers should offer the smallest possible amount. Traditional, deterministic models of evolutionary game theory agree: in the one-shot anonymous Ultimatum Game, natural selection favors low offers and demands. Experiments instead show a preference for fairness: often responders reject low offers and proposers make higher offers than needed to avoid rejection. Here we show that using stochastic evolutionary game theory, where agents make mistakes when judging the payoffs and strategies of others, natural selection favors fairness. Across a range of parameters, the average strategy matches the observed behavior: proposers offer between 30% and 50%, and responders demand between 25% and 40%. Rejecting low offers increases relative payoff in pairwise competition between two strategies and is favored when selection is sufficiently weak. Offering more than you demand increases payoff when many strategies are present simultaneously and is favored when mutation is sufficiently high. We also perform a behavioral experiment and find empirical support for these theoretical findings: uncertainty about the success of others is associated with higher demands and offers; and inconsistency in the behavior of others is associated with higher offers but not predictive of demands. In an uncertain world, fairness finishes first. PMID:23341593

Evolution of fairness in the one-shot anonymous Ultimatum Game.

PubMed

Rand, David G; Tarnita, Corina E; Ohtsuki, Hisashi; Nowak, Martin A

2013-02-12

Classical economic models assume that people are fully rational and selfish, while experiments often point to different conclusions. A canonical example is the Ultimatum Game: one player proposes a division of a sum of money between herself and a second player, who either accepts or rejects. Based on rational self-interest, responders should accept any nonzero offer and proposers should offer the smallest possible amount. Traditional, deterministic models of evolutionary game theory agree: in the one-shot anonymous Ultimatum Game, natural selection favors low offers and demands. Experiments instead show a preference for fairness: often responders reject low offers and proposers make higher offers than needed to avoid rejection. Here we show that using stochastic evolutionary game theory, where agents make mistakes when judging the payoffs and strategies of others, natural selection favors fairness. Across a range of parameters, the average strategy matches the observed behavior: proposers offer between 30% and 50%, and responders demand between 25% and 40%. Rejecting low offers increases relative payoff in pairwise competition between two strategies and is favored when selection is sufficiently weak. Offering more than you demand increases payoff when many strategies are present simultaneously and is favored when mutation is sufficiently high. We also perform a behavioral experiment and find empirical support for these theoretical findings: uncertainty about the success of others is associated with higher demands and offers; and inconsistency in the behavior of others is associated with higher offers but not predictive of demands. In an uncertain world, fairness finishes first.

Effect of intermediate defense measures in voluntary vaccination games

NASA Astrophysics Data System (ADS)

Iwamura, Yoshiro; Tanimoto, Jun; Fukuda, Eriko

2016-09-01

We build a model to reproduce the decision-making process of getting a vaccination based on the evolutionary game theory dovetailed with the SIR model for epidemic spreading. Unlike the two extreme options of whether or not getting a vaccination leads to perfect immunity, we consider whether ‘intermediate defense measures’ including masking, gargling, and hand-washing lead to imperfect effects of preventing infection. We consider introducing not only a ‘third strategy’ as a discrete intermediate measure but also a continuous strategy space connecting the cases of getting and not getting a vaccination. Interestingly, our evolutionary analysis suggests that the introduction of intermediate measures makes no difference for the case of a 2-strategy system in which only either getting or not getting a vaccination is allowed, even does not ameliorate, or say, gets worse to prevent spreading a disease. This seems quite different from what was observed in 2-player and 2-strategy (2  ×  2) prisoner’s dilemma (PD) games with relatively stronger chicken-type dilemma than the stag-hunt one in which the introduction of middle-course strategies significantly enhances cooperation.

On Nash Equilibrium and Evolutionarily Stable States That Are Not Characterised by the Folk Theorem

PubMed Central

Li, Jiawei; Kendall, Graham

2015-01-01

In evolutionary game theory, evolutionarily stable states are characterised by the folk theorem because exact solutions to the replicator equation are difficult to obtain. It is generally assumed that the folk theorem, which is the fundamental theory for non-cooperative games, defines all Nash equilibria in infinitely repeated games. Here, we prove that Nash equilibria that are not characterised by the folk theorem do exist. By adopting specific reactive strategies, a group of players can be better off by coordinating their actions in repeated games. We call it a type-k equilibrium when a group of k players coordinate their actions and they have no incentive to deviate from their strategies simultaneously. The existence and stability of the type-k equilibrium in general games is discussed. This study shows that the sets of Nash equilibria and evolutionarily stable states have greater cardinality than classic game theory has predicted in many repeated games. PMID:26288088

Evolutionary game theory: molecules as players.

PubMed

Bohl, Katrin; Hummert, Sabine; Werner, Sarah; Basanta, David; Deutsch, Andreas; Schuster, Stefan; Theissen, Günter; Schroeter, Anja

2014-12-01

In this and an accompanying paper we review the use of game theoretical concepts in cell biology and molecular biology. This review focuses on the subcellular level by considering viruses, genes, and molecules as players. We discuss in which way catalytic RNA can be treated by game theory. Moreover, genes can compete for success in replication and can have different strategies in interactions with other genetic elements. Also transposable elements, or "jumping genes", can act as players because they usually bear different traits or strategies. Viruses compete in the case of co-infecting a host cell. Proteins interact in a game theoretical sense when forming heterodimers. Finally, we describe how the Shapley value can be applied to enzymes in metabolic pathways. We show that game theory can be successfully applied to describe and analyse scenarios at the molecular level resulting in counterintuitive conclusions.

Eco-evolutionary spatial dynamics in the Glanville fritillary butterfly.

PubMed

Hanski, Ilkka A

2011-08-30

Demographic population dynamics, gene flow, and local adaptation may influence each other and lead to coupling of ecological and evolutionary dynamics, especially in species inhabiting fragmented heterogeneous environments. Here, I review long-term research on eco-evolutionary spatial dynamics in the Glanville fritillary butterfly inhabiting a large network of approximately 4,000 meadows in Finland. The metapopulation persists in a balance between frequent local extinctions and recolonizations. The genetic spatial structure as defined by neutral markers is much more coarse-grained than the demographic spatial structure determined by the fragmented habitat, yet small-scale spatial structure has important consequences for the dynamics. I discuss three examples of eco-evolutionary spatial dynamics. (i) Extinction-colonization metapopulation dynamics influence allele frequency changes in the phosphoglucose isomerase (Pgi) gene, which leads to strong associations between genetic variation in Pgi and dispersal, recolonization, and local population dynamics. (ii) Inbreeding in local populations increases their risk for extinction, whereas reciprocal effects between inbreeding, population size, and emigration represent likely eco-evolutionary feedbacks. (iii) Genetically determined female oviposition preference for two host plant species exhibits a cline paralleling a gradient in host plant relative abundances, and host plant preference of dispersing females in relation to the host plant composition of habitat patches influences immigration (gene flow) and recolonization (founder events). Eco-evolutionary spatial dynamics in heterogeneous environments may not lead to directional evolutionary changes unless the environment itself changes, but eco-evolutionary dynamics may contribute to the maintenance of genetic variation attributable to fluctuating selection in space and time.

Theoretical and Experimental Analysis of an Evolutionary Social-Learning Game

DTIC Science & Technology

2012-01-13

Nettle outlines the circumstances in which verbal communication is evolutionarily adaptive, and why few species have developed the ability to use...language despite its apparent advantages [28]. Nettle uses a significantly simpler model than the Cultaptation game, but provides insight that may be useful...provided by Kearns et al. was designed as an online algorithm, so it only returns the near-optimal action for the state at the root of the search tree

Spatial evolutionary games with weak selection.

PubMed

Nanda, Mridu; Durrett, Richard

2017-06-06

Recently, a rigorous mathematical theory has been developed for spatial games with weak selection, i.e., when the payoff differences between strategies are small. The key to the analysis is that when space and time are suitably rescaled, the spatial model converges to the solution of a partial differential equation (PDE). This approach can be used to analyze all [Formula: see text] games, but there are a number of [Formula: see text] games for which the behavior of the limiting PDE is not known. In this paper, we give rules for determining the behavior of a large class of [Formula: see text] games and check their validity using simulation. In words, the effect of space is equivalent to making changes in the payoff matrix, and once this is done, the behavior of the spatial game can be predicted from the behavior of the replicator equation for the modified game. We say predicted here because in some cases the behavior of the spatial game is different from that of the replicator equation for the modified game. For example, if a rock-paper-scissors game has a replicator equation that spirals out to the boundary, space stabilizes the system and produces an equilibrium.

Spatial evolutionary games with weak selection

PubMed Central

Nanda, Mridu; Durrett, Richard

2017-01-01

Recently, a rigorous mathematical theory has been developed for spatial games with weak selection, i.e., when the payoff differences between strategies are small. The key to the analysis is that when space and time are suitably rescaled, the spatial model converges to the solution of a partial differential equation (PDE). This approach can be used to analyze all 2×2 games, but there are a number of 3×3 games for which the behavior of the limiting PDE is not known. In this paper, we give rules for determining the behavior of a large class of 3×3 games and check their validity using simulation. In words, the effect of space is equivalent to making changes in the payoff matrix, and once this is done, the behavior of the spatial game can be predicted from the behavior of the replicator equation for the modified game. We say predicted here because in some cases the behavior of the spatial game is different from that of the replicator equation for the modified game. For example, if a rock–paper–scissors game has a replicator equation that spirals out to the boundary, space stabilizes the system and produces an equilibrium. PMID:28533405

Unfavorable Individuals in Social Gaming Networks.

PubMed

Zhang, Yichao; Chen, Guanrong; Guan, Jihong; Zhang, Zhongzhi; Zhou, Shuigeng

2015-12-09

In social gaming networks, the current research focus has been on the origin of widespread reciprocal behaviors when individuals play non-cooperative games. In this paper, we investigate the topological properties of unfavorable individuals in evolutionary games. The unfavorable individuals are defined as the individuals gaining the lowest average payoff in a round of game. Since the average payoff is normally considered as a measure of fitness, the unfavorable individuals are very likely to be eliminated or change their strategy updating rules from a Darwinian perspective. Considering that humans can hardly adopt a unified strategy to play with their neighbors, we propose a divide-and-conquer game model, where individuals can interact with their neighbors in the network with appropriate strategies. We test and compare a series of highly rational strategy updating rules. In the tested scenarios, our analytical and simulation results surprisingly reveal that the less-connected individuals in degree-heterogeneous networks are more likely to become the unfavorable individuals. Our finding suggests that the connectivity of individuals as a social capital fundamentally changes the gaming environment. Our model, therefore, provides a theoretical framework for further understanding the social gaming networks.

Unfavorable Individuals in Social Gaming Networks

NASA Astrophysics Data System (ADS)

Zhang, Yichao; Chen, Guanrong; Guan, Jihong; Zhang, Zhongzhi; Zhou, Shuigeng

2015-12-01

In social gaming networks, the current research focus has been on the origin of widespread reciprocal behaviors when individuals play non-cooperative games. In this paper, we investigate the topological properties of unfavorable individuals in evolutionary games. The unfavorable individuals are defined as the individuals gaining the lowest average payoff in a round of game. Since the average payoff is normally considered as a measure of fitness, the unfavorable individuals are very likely to be eliminated or change their strategy updating rules from a Darwinian perspective. Considering that humans can hardly adopt a unified strategy to play with their neighbors, we propose a divide-and-conquer game model, where individuals can interact with their neighbors in the network with appropriate strategies. We test and compare a series of highly rational strategy updating rules. In the tested scenarios, our analytical and simulation results surprisingly reveal that the less-connected individuals in degree-heterogeneous networks are more likely to become the unfavorable individuals. Our finding suggests that the connectivity of individuals as a social capital fundamentally changes the gaming environment. Our model, therefore, provides a theoretical framework for further understanding the social gaming networks.

Maximal aggregation of polynomial dynamical systems

PubMed Central

Cardelli, Luca; Tschaikowski, Max

2017-01-01

Ordinary differential equations (ODEs) with polynomial derivatives are a fundamental tool for understanding the dynamics of systems across many branches of science, but our ability to gain mechanistic insight and effectively conduct numerical evaluations is critically hindered when dealing with large models. Here we propose an aggregation technique that rests on two notions of equivalence relating ODE variables whenever they have the same solution (backward criterion) or if a self-consistent system can be written for describing the evolution of sums of variables in the same equivalence class (forward criterion). A key feature of our proposal is to encode a polynomial ODE system into a finitary structure akin to a formal chemical reaction network. This enables the development of a discrete algorithm to efficiently compute the largest equivalence, building on approaches rooted in computer science to minimize basic models of computation through iterative partition refinements. The physical interpretability of the aggregation is shown on polynomial ODE systems for biochemical reaction networks, gene regulatory networks, and evolutionary game theory. PMID:28878023

Holistic Darwinism: the new evolutionary paradigm and some implications for political science.

PubMed

Corning, Peter A

2008-03-01

Holistic Darwinism is a candidate name for a major paradigm shift that is currently underway in evolutionary biology and related disciplines. Important developments include (1) a growing appreciation for the fact that evolution is a multilevel process, from genes to ecosystems, and that interdependent coevolution is a ubiquitous phenomenon in nature; (2) a revitalization of group selection theory, which was banned (prematurely) from evolutionary biology over 30 years ago (groups may in fact be important evolutionary units); (3) a growing respect for the fact that the genome is not a "bean bag" (in biologist Ernst Mayr's caricature), much less a gladiatorial arena for competing selfish genes, but a complex, interdependent, cooperating system; (4) an increased recognition that symbiosis is an important phenomenon in nature and that symbiogenesis is a major source of innovation in evolution; (5) an array of new, more advanced game theory models, which support the growing evidence that cooperation is commonplace in nature and not a rare exception; (6) new research and theoretical work that stresses the role of nurture in evolution, including developmental processes, phenotypic plasticity, social information transfer (culture), and especially the role of behavioral innovations as pacemakers of evolutionary change (e.g., niche construction theory, which is concerned with the active role of organisms in shaping the evolutionary process, and gene-culture coevolution theory, which relates especially to the dynamics of human evolution); (7) and, not least, a broad effort to account for the evolution of biological complexity--from major transition theory to the "Synergism Hypothesis." Here I will briefly review these developments and will present a case for the proposition that this paradigm shift has profound implications for the social sciences, including specifically political theory, economic theory, and political science as a discipline. Interdependent superorganisms, it turns out, have played a major role in evolution--from eukaryotes to complex human societies.