Emergence of cooperation through coevolving time scale in spatial prisoner's dilemma.

We study evolutionary prisoner's dilemma game by considering adaptive strategy-selection time scale among individuals according to a "win-slower, lose-faster" rule: if an individual successfully resists the invasion of an opponent, she is prone to hold her strategy for longer time through decreasing her strategy-selection time scale; otherwise, she increases the time scale because of losing. We find that the greater the losers increase their strategy-selection time scales, the better for cooperation. Interestingly, optimal cooperation can be induced by proper adaptive rate in the strategy-selection time scale. Our results may have potential implications in the design of consensus protocol in multiagent systems.

[1]  M. Perc.  Coherence resonance in a spatial prisoner's dilemma game , 2006 .

[2]  Ángel Sánchez,et al.  Imperfect imitation can enhance cooperation , 2009, ArXiv.

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

[4]  G. Szabó,et al.  Evolutionary games on graphs , 2006, cond-mat/0607344.

[5]  Michael Doebeli,et al.  Spatial structure often inhibits the evolution of cooperation in the snowdrift game , 2004, Nature.

[6]  Shahar Hod,et al.  Self-segregation versus clustering in the evolutionary minority game. , 2002, Physical review letters.

[7]  Long Wang,et al.  Promotion of cooperation induced by appropriate payoff aspirations in a small-world networked game. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[8]  Yinghai Wang,et al.  Diversity of rationality affects the evolution of cooperation. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[10]  Matjaž Perc,et al.  Evolutionary and dynamical coherence resonances in the pair approximated prisoner's dilemma game , 2006 .

[11]  Arne Traulsen,et al.  Similarity-based cooperation and spatial segregation. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[13]  Y Moreno,et al.  Effects of mobility in a population of prisoner's dilemma players. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  Arne Traulsen,et al.  Coevolution of strategy and structure in complex networks with dynamical linking. , 2006, Physical review letters.

[15]  C. Hauert,et al.  Reputation-based partner choice promotes cooperation in social networks. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[17]  Francisco C. Santos,et al.  Cooperation Prevails When Individuals Adjust Their Social Ties , 2006, PLoS Comput. Biol..

[18]  Víctor M Eguíluz,et al.  Cooperation, social networks, and the emergence of leadership in a prisoner's dilemma with adaptive local interactions. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[19]  Víctor M Eguíluz,et al.  Coevolution of dynamical states and interactions in dynamic networks. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[20]  Mao-Bin Hu,et al.  Asymmetric cost in snowdrift game on scale-free networks , 2009 .

[21]  J Gómez-Gardeñes,et al.  Dynamical organization of cooperation in complex topologies. , 2007, Physical review letters.

[22]  Zhihai Rong,et al.  Diversity of reproduction time scale promotes cooperation in spatial prisoner's dilemma games. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[23]  Zhi-Xi Wu,et al.  Evolutionary prisoner's dilemma game with dynamic preferential selection. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[24]  J. J. Arenzon,et al.  Does mobility decrease cooperation? , 2006, Journal of theoretical biology.

[25]  G. Szabo,et al.  Diversity of reproduction rate supports cooperation in the prisoner's dilemma game on complex networks , 2008, 0802.2807.

[26]  G. Szabó,et al.  Cooperation enhanced by inhomogeneous activity of teaching for evolutionary Prisoner's Dilemma games , 2006, q-bio/0610001.

[27]  C. Hauert,et al.  Models of cooperation based on the Prisoner's Dilemma and the Snowdrift game , 2005 .

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

[29]  J. Cuesta,et al.  Time scales in evolutionary dynamics. , 2006, Physical review letters.

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

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

[32]  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.

[33]  Ángel Sánchez,et al.  Evolutionary game theory: Temporal and spatial effects beyond replicator dynamics , 2009, Physics of life reviews.

[34]  Claus O Wilke,et al.  Maternal effects in molecular evolution. , 2001, Physical review letters.

[35]  P. Holme,et al.  Effects of strategy-migration direction and noise in the evolutionary spatial prisoner's dilemma. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  G. Szabó,et al.  Cooperation in the noisy case: Prisoner's dilemma game on two types of regular random graphs. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[37]  M. Kuperman,et al.  Social games in a social network. , 2000, Physical review. E, Statistical, nonlinear, and soft matter physics.

[38]  Attila Szolnoki,et al.  Evolutionary prisoner's dilemma game on Newman-Watts networks. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[39]  G. Szabó,et al.  Cooperation in spatial prisoner's dilemma with two types of players for increasing number of neighbors. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  G. Szabó,et al.  Phase diagrams for an evolutionary prisoner's dilemma game on two-dimensional lattices. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[41]  Xiaoming Zhang,et al.  How scale-free networks and large-scale collective cooperation emerge in complex homogeneous social systems. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[42]  Jörgen W. Weibull,et al.  Evolutionary Game Theory , 1996 .

[43]  F C Santos,et al.  Epidemic spreading and cooperation dynamics on homogeneous small-world networks. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[44]  Long Wang,et al.  Interaction stochasticity supports cooperation in spatial Prisoner's dilemma. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[45]  Reza Olfati-Saber,et al.  Consensus and Cooperation in Networked Multi-Agent Systems , 2007, Proceedings of the IEEE.

[46]  D. Helbing,et al.  The outbreak of cooperation among success-driven individuals under noisy conditions , 2009, Proceedings of the National Academy of Sciences.

[47]  G. Szabó,et al.  Evolutionary prisoner's dilemma game on a square lattice , 1997, cond-mat/9710096.

[48]  Guanrong Chen,et al.  Phase transition and hysteresis loop in structured games with global updating. , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[50]  Feng Qi,et al.  Randomness enhances cooperation: a resonance-type phenomenon in evolutionary games. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[52]  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.

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

[54]  G. Szabó,et al.  Impact of aging on the evolution of cooperation in the spatial prisoner's dilemma game. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[55]  C. Hauert,et al.  Game theory and physics , 2005 .