Coevolution of cooperation and network structure in social dilemmas in evolutionary dynamic complex network

Emergence of cooperation in social dilemmas is an essential phenomena for the functioning of numerous multilevel and complex systems. The evidence of cooperation ranges from the elementary biological organisms to the most sophisticated human societies. Although emergence of cooperation is widely experienced, but its evolution is not well explained, since natural selection typically promotes selfish behaviours which are often not socially optimal. In this paper the coevolution of network structure and emergence of cooperation is studied in four classes of social dilemmas, representing the prisoner's dilemma, Hawk–Dove, snowdrift and coordination classes of games, in structured populations defined by weighted complex networks. The strength of interaction between two individuals is represented by network (edge) weight, which changes according to individuals’ preference through the evolutionary network dynamics. Using evolutionary dynamic network based simulations of the games model on randomly weighted complete networks, we present a detailed study of the evolution of dynamic complex network through the evolution of the structural properties of a network, such as clustering coefficient, assortativity coefficient, entropy of degree distribution, average strength of interaction and the promotion of cooperative behaviour in all four classes of games. The effect of changing the cost-to-benefit ratio on these network properties and evolution of cooperation is also reported.

[1]  Albert-László Barabási,et al.  Statistical mechanics of complex networks , 2001, ArXiv.

[2]  Gerald S. Wilkinson,et al.  Food Sharing in Vampire Bats , 1990 .

[3]  E. Fehr,et al.  Altruistic punishment in humans , 2002, Nature.

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

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

[6]  C. Hauert,et al.  Via Freedom to Coercion: The Emergence of Costly Punishment , 2007, Science.

[7]  Swami Iyer,et al.  Evolution of Cooperation in Social Dilemmas on Complex Networks , 2016, PLoS Comput. Biol..

[8]  Matjaz Perc,et al.  Statistical physics of crime: A review , 2014, Physics of life reviews.

[9]  J. Neumann,et al.  Prisoner's Dilemma , 1993 .

[10]  Margarita Ifti,et al.  Effects of neighbourhood size and connectivity on the spatial Continuous Prisoner's Dilemma. , 2004, Journal of theoretical biology.

[11]  M. Perc,et al.  Social diversity and promotion of cooperation in the spatial prisoner's dilemma game. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[12]  J M Smith,et al.  Evolution and the theory of games , 1976 .

[13]  Attila Szolnoki,et al.  Making new connections towards cooperation in the prisoner's dilemma game , 2008, 0811.4372.

[14]  Attila Szolnoki,et al.  Coevolutionary success-driven multigames , 2014, ArXiv.

[15]  M. Nowak,et al.  Evolution of cooperation by multilevel selection. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[16]  M. Eigen,et al.  The Hypercycle: A principle of natural self-organization , 2009 .

[17]  M E J Newman.  Assortative mixing in networks. , 2002, Physical review letters.

[18]  Josef Hofbauer,et al.  Evolutionary Games and Population Dynamics , 1998 .

[19]  Attila Szolnoki,et al.  Resolving social dilemmas on evolving random networks , 2009, 0910.1905.

[20]  Attila Szolnoki,et al.  Coevolutionary Games - A Mini Review , 2009, Biosyst..

[21]  Martin A. Nowak,et al.  Spatial structure often inhibits the evolution of cooperation in the snowdrift game , 2022 .

[22]  M. Perc,et al.  Promoting cooperation in social dilemmas via simple coevolutionary rules , 2008, 0812.1122.

[23]  W. Hamilton.  The genetical evolution of social behaviour. I. , 1964, Journal of theoretical biology.

[24]  Matjaž Perc,et al.  Phase transitions in models of human cooperation , 2016 .

[25]  Attila Szolnoki,et al.  Evolutionary dynamics of group interactions on structured populations: a review , 2013, Journal of The Royal Society Interface.

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

[27]  Changshui Zhang,et al.  Learning and Innovative Elements of Strategy Adoption Rules Expand Cooperative Network Topologies , 2007, PloS one.

[28]  M. Nowak,et al.  Evolution of indirect reciprocity by image scoring , 1998, Nature.

[29]  Peter Schuster,et al.  A principle of natural self-organization , 1977, Naturwissenschaften.

[30]  Attila Szolnoki,et al.  Statistical Physics of Human Cooperation , 2017, ArXiv.

[31]  M. Perc,et al.  Coevolution of teaching activity promotes cooperation , 2008, 0803.4091.

[32]  M. Perc.  Evolution of cooperation on scale-free networks subject to error and attack , 2009, 0902.4661.

[33]  Eörs Szathmáry,et al.  The Major Transitions in Evolution , 1997 .

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

[35]  M. Doebeli,et al.  Spatial evolutionary game theory: Hawks and Doves revisited , 1996, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[36]  J. M. Smith,et al.  The Logic of Animal Conflict , 1973, Nature.

[37]  H. Young,et al.  The Evolution of Conventions , 1993 .

[38]  Wei Chen,et al.  Coevolution of aspirations and cooperation in spatial prisoner's dilemma game , 2015 .

[39]  G. Caldarelli,et al.  Assortative model for social networks. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  David Cornforth,et al.  Asynchronous spatial evolutionary games: spatial patterns, Diversity and Chaos , 2007, 2007 IEEE Congress on Evolutionary Computation.

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

[42]  F. C. Santos,et al.  Scale-free networks provide a unifying framework for the emergence of cooperation. , 2005, Physical review letters.

[43]  Chonghui Guo,et al.  Entropy optimization of scale-free networks’ robustness to random failures , 2005, cond-mat/0506725.

[44]  T. Killingback,et al.  Evolution in group-structured populations can resolve the tragedy of the commons , 2006, Proceedings of the Royal Society B: Biological Sciences.

[45]  T. Killingback,et al.  An Application of Evolutionary Game Theory to Social Dilemmas: The Traveler's Dilemma and the Minimum Effort Coordination Game , 2014, PloS one.

[46]  M. Perc,et al.  Emergence of multilevel selection in the prisoner's dilemma game on coevolving random networks , 2009, 0909.4019.

[47]  M. Perc,et al.  Towards effective payoffs in the prisoner’s dilemma game on scale-free networks , 2007, 0711.4028.

[48]  György Szabó,et al.  Evolutionary prisoner's dilemma games with voluntary participation. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[49]  Duncan J. Watts,et al.  Collective dynamics of ‘small-world’ networks , 1998, Nature.

[50]  F. C. Santos,et al.  Evolutionary dynamics of social dilemmas in structured heterogeneous populations. , 2006, Proceedings of the National Academy of Sciences of the United States of America.

[51]  Albert,et al.  Emergence of scaling in random networks , 1999, Science.

[52]  K. Sigmund.  The Calculus of Selfishness , 2010 .

[53]  Wen-Xu Wang,et al.  Effects of average degree on cooperation in networked evolutionary game , 2006 .

[54]  M. Nowak.  Evolutionary Dynamics: Exploring the Equations of Life , 2006 .

[55]  Benjamin L. Hart,et al.  Reciprocal Allogrooming in Wild Impala Lambs , 2010 .

[56]  B. Skyrms.  The Stag Hunt and the Evolution of Social Structure , 2003 .

[57]  Swami Iyer,et al.  Evolutionary dynamics of the traveler's dilemma and minimum-effort coordination games on complex networks. , 2014, Physical review. E, Statistical, nonlinear, and soft matter physics.

[58]  Günther Palm,et al.  Evolutionary stable strategies and game dynamics for n-person games , 1984 .

[59]  M. Nowak,et al.  SuperCooperators: Altruism, Evolution, and Why We Need Each Other to Succeed , 2011 .

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

[61]  Wenxu Wang,et al.  Memory-based snowdrift game on networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[62]  Paul E. Turner,et al.  Prisoner's dilemma in an RNA virus , 1999, Nature.

[63]  H. Young,et al.  Individual Strategy and Social Structure: An Evolutionary Theory of Institutions , 1999 .