Strategy-updating depending on local environment enhances cooperation in prisoner's dilemma game

A new method of strategy updating is proposed in the prisoners dilemma game.Some players apply the replicator dynamic rule for strategy updating, while the others utilize the comprehensive method.The intelligent players would consider not only the neighbors payoff but also its environment.The results indicate that with the increase of intelligent players, the fraction of cooperation increases. An evolutionary prisoners dilemma game is studied on a square lattice when local environment is considered. And a new strategy updating rule is utilized in this game. First, individuals are classified as two classes: stochastic players and intelligent players. The stochastic players are the ones who adopt the rule of replicator dynamics to update strategies, and the intelligent players are those who make a decision through comprehensive considerations of the local environment (namely, the information of different-strategy neighbors environment). Second, the intelligent players evaluation is calculated from payoffs and local environment by DempsterShafer theory. The results indicate that the new strategy-updating method promotes cooperation when intelligent individuals utilize the information of different-strategy neighborhoods. Moreover, the increasing number of intelligent player promotes cooperation level. Furthermore, it is noteworthy that cooperators will finally coexist with defectors no matter what the proportion of intelligence is, which is worthy to think about.

[1]  Wen-Xu Wang,et al.  Role of adaptive migration in promoting cooperation in spatial games. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Xinyang Deng,et al.  Matrix games with payoffs of belief structures , 2016, Appl. Math. Comput..

[3]  S. Bowles.  Did Warfare Among Ancestral Hunter-Gatherers Affect the Evolution of Human Social Behaviors? , 2009, Science.

[4]  Yong Deng,et al.  A new fuzzy dempster MCDM method and its application in supplier selection , 2011, Expert Syst. Appl..

[5]  C. K. Michael Tse,et al.  Community structure promotes the emergence of persistence behavior in social networks , 2015, 2015 IEEE International Symposium on Circuits and Systems (ISCAS).

[6]  Xiang Li,et al.  Roles of mixing patterns in cooperation on a scale-free networked game. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[7]  Alasdair I. Houston,et al.  Variation in behaviour promotes cooperation in the Prisoner's Dilemma game , 2004, Nature.

[8]  C. Hauert,et al.  Volunteering as Red Queen Mechanism for Cooperation in Public Goods Games , 2002, Science.

[9]  Lin Wang,et al.  Degree mixing in multilayer networks impedes the evolution of cooperation , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[10]  Lin Wang,et al.  Evolutionary games on multilayer networks: a colloquium , 2015, The European Physical Journal B.

[11]  R. Riolo,et al.  Evolution of cooperation without reciprocity , 2001, Nature.

[12]  M. Nowak,et al.  The evolution of eusociality , 2010, Nature.

[13]  Zhihai Rong,et al.  Cooperation percolation in spatial prisoner's dilemma game , 2015, 1503.00143.

[14]  Xiaoping Zheng,et al.  Effect of heterogeneous sub-populations on the evolution of cooperation , 2015, Appl. Math. Comput..

[15]  Zhihai Rong,et al.  Boosting cooperation by involving extortion in spatial prisoner's dilemma games. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[16]  Bing-Hong Wang,et al.  Uncovering cooperative behaviors with sparse historical behavior data in the spatial games , 2015, Appl. Math. Comput..

[17]  Jun Tanimoto,et al.  Effect of Initial Fraction of Cooperators on Cooperative Behavior in Evolutionary Prisoner's Dilemma Game , 2013, PloS one.

[18]  M. Nowak.  Five Rules for the Evolution of Cooperation , 2006, Science.

[19]  Dawei Zhao,et al.  Statistical physics of vaccination , 2016, ArXiv.

[20]  M. Nowak,et al.  A strategy of win-stay, lose-shift that outperforms tit-for-tat in the Prisoner's Dilemma game , 1993, Nature.

[21]  Laurent Lehmann,et al.  Inclusive fitness theory and eusociality , 2011, Nature.

[22]  Wen-Xu Wang,et al.  Feedback reciprocity mechanism promotes the cooperation of highly clustered scale-free networks. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Dong Hao,et al.  Diversity of timescale promotes the maintenance of extortioners in a spatial prisoner’s dilemma game , 2015 .

[24]  Guanrong Chen,et al.  Coevolution of strategy-selection time scale and cooperation in spatial prisoner's dilemma game , 2013 .

[25]  H. Gintis,et al.  A Cooperative Species: Human Reciprocity and Its Evolution , 2011 .

[26]  Matjaz Perc,et al.  Evolutionary mixed games in structured populations: Cooperation and the benefits of heterogeneity , 2016, Physical review. E.

[27]  Essam S. El-Sedy,et al.  The payoff matrix of repeated asymmetric 2×2 games , 2016, Appl. Math. Comput..

[28]  Rachid Belaroussi,et al.  Multi-Hypotheses Tracking using the Dempster-Shafer Theory, application to ambiguous road context , 2016, Inf. Fusion.

[29]  Jing Ma,et al.  An evolutionary game for the diffusion of rumor in complex networks , 2015 .

[30]  J. André,et al.  Models of the evolution of fairness in the ultimatum game: a review and classification , 2016 .

[31]  M. Nowak,et al.  Evolution of indirect reciprocity , 2005, Nature.

[32]  M. Barnsley,et al.  Chaos game for IFSs on topological spaces , 2014, 1410.3962.

[33]  F. Weissing,et al.  Negotiation and appeasement can be more effective drivers of sociality than kin selection , 2016, Philosophical Transactions of the Royal Society B: Biological Sciences.

[34]  M. Beynon,et al.  The Dempster-Shafer theory of evidence: an alternative approach to multicriteria decision modelling , 2000 .

[35]  A. van Oudenaarden,et al.  Snowdrift game dynamics and facultative cheating in yeast , 2009, Nature.

[36]  Martin A. Nowak,et al.  Evolutionary dynamics on graphs , 2005, Nature.

[37]  C. Darwin.  The Origin of Species by Means of Natural Selection, Or, The Preservation of Favoured Races in the Struggle for Life , 2019 .

[38]  M. Nowak,et al.  Tit for tat in heterogeneous populations , 1992, Nature.

[39]  Juan Wang,et al.  Evolution of cooperation in the spatial public goods game with adaptive reputation assortment , 2016 .

[40]  Zi Yu,et al.  An improved fitness evaluation mechanism with noise in prisoner's dilemma game , 2016, Appl. Math. Comput..

[41]  Yi Yu,et al.  System crash as dynamics of complex networks , 2016, Proceedings of the National Academy of Sciences.

[42]  Michael Tomasello,et al.  Chimpanzees coordinate in a snowdrift game , 2016, Animal Behaviour.

[43]  Attila Szolnoki,et al.  Rewarding evolutionary fitness with links between populations promotes cooperation , 2014, Journal of theoretical biology.

[44]  S. West,et al.  Conditional cooperation and confusion in public-goods experiments , 2016, Proceedings of the National Academy of Sciences.

[45]  S. Kokubo,et al.  Universal scaling for the dilemma strength in evolutionary games. , 2015, Physics of life reviews.

[46]  W. Hamilton,et al.  The Evolution of Cooperation , 1984 .

[47]  Essam S. El-Sedy,et al.  Two population three-player prisoner's dilemma game , 2016, Appl. Math. Comput..

[48]  Yin Zhong,et al.  Extended s-wave pairing symmetry on the triangular lattice heavy fermion system , 2015 .

[49]  Jonathan D. Cohen,et al.  The Neural Basis of Economic Decision-Making in the Ultimatum Game , 2003, Science.

[50]  Tadeusz Platkowski,et al.  Egalitarian solutions to multiperson social dilemmas in populations , 2016, Appl. Math. Comput..

[51]  Lin Wang,et al.  Coupled disease–behavior dynamics on complex networks: A review , 2015, Physics of Life Reviews.

[52]  Xinyang Deng,et al.  Comprehensive consideration of strategy updating promotes cooperation in the prisoner’s dilemma game , 2014 .

[53]  Tao Wang,et al.  Behavioral evolution in evacuation crowd based on heterogeneous rationality of small groups , 2015, Appl. Math. Comput..

[54]  Yong Deng,et al.  Generalized evidence theory , 2014, Applied Intelligence.

[55]  M. Nowak,et al.  Evolutionary games and spatial chaos , 1992, Nature.

[56]  Attila Szolnoki,et al.  Different perceptions of social dilemmas: Evolutionary multigames in structured populations , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[57]  G. Szabó,et al.  Selection of dynamical rules in spatial Prisoner's Dilemma games , 2009, 0911.0661.

[58]  Attila Szolnoki,et al.  Self-organization towards optimally interdependent networks by means of coevolution , 2014, ArXiv.

[59]  Glenn Shafer,et al.  A Mathematical Theory of Evidence , 2020, A Mathematical Theory of Evidence.

[60]  Arthur P. Dempster,et al.  Upper and Lower Probabilities Induced by a Multivalued Mapping , 1967, Classic Works of the Dempster-Shafer Theory of Belief Functions.