Cooperation enhanced by moderate tolerance ranges in myopically selective interactions.

We present a mode of myopically selective interaction to study the evolutionary prisoner's dilemma game in scale-free networks. Each individual has a reputation-based tolerance range and only tends to interact with the neighbors whose reputation is within its tolerance range. Moreover, its reputation is assessed in response to the interactions in the neighborhood. Interestingly, we show that moderate values of tolerance range can result in the best promotion of cooperation due to the emergence of group selection mechanism. Furthermore, we study the effects of weighting factor in the assessment rule of reputation on the evolution of cooperation. We also show how cooperation evolves in some extended situations, where an interaction stimulus payment is considered for individuals, and where the strategy and reputation of individuals can spread simultaneously. Our results may enhance the understanding of evolutionary dynamics in graph-structured populations where individuals conditionally play with their neighbors according to some myopic selection criteria.

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

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

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

[4]  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.

[5]  Zhi-Xi Wu,et al.  Evolutionary prisoner's dilemma game on BarabsiAlbert scale-free networks , 2007 .

[6]  Martin A Nowak,et al.  Spatial invasion of cooperation. , 2008, Journal of theoretical biology.

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

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

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

[10]  N. Masuda Participation costs dismiss the advantage of heterogeneous networks in evolution of cooperation , 2007, Proceedings of the Royal Society B: Biological Sciences.

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

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

[13]  Zhi-Xi Wu,et al.  Cooperation enhanced by the difference between interaction and learning neighborhoods for evolutionary spatial prisoner's dilemma games. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[14]  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.

[15]  H. Ohtsuki,et al.  Breaking the symmetry between interaction and replacement in evolutionary dynamics on graphs. , 2007, Physical review letters.

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

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

[18]  Arne Traulsen,et al.  Stochastic payoff evaluation increases the temperature of selection. , 2007, Journal of theoretical biology.

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

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

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

[22]  Arne Traulsen,et al.  Stochastic sampling of interaction partners versus deterministic payoff assignment. , 2009, Journal of theoretical biology.

[23]  J. Sullivan,et al.  The psychological underpinnings of democracy: A selective review of research on political tolerance, interpersonal trust, and social capital. , 1999, Annual review of psychology.

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

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

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

[27]  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.

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

[29]  J. J. Arenzon,et al.  Random mobility and spatial structure often enhance cooperation. , 2008, Journal of theoretical biology.

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

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

[32]  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.

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

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

[35]  Mei Zhang,et al.  Random partnerships in spatial game theory. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[37]  F. C. Santos,et al.  A new route to the evolution of cooperation , 2006, Journal of evolutionary biology.

[38]  Dirk Helbing,et al.  Pattern formation, social forces, and diffusion instability in games with success-driven motion , 2009, 0903.0928.

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

[40]  Angel Sánchez,et al.  Evolving learning rules and emergence of cooperation in spatial prisoner's dilemma. , 2008, Journal of theoretical biology.

[41]  F. C. Santos,et al.  Graph topology plays a determinant role in the evolution of cooperation , 2006, Proceedings of the Royal Society B: Biological Sciences.

[42]  F. C. Santos,et al.  Social diversity promotes the emergence of cooperation in public goods games , 2008, Nature.

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

[44]  Martin A Nowak,et al.  Evolutionary graph theory: breaking the symmetry between interaction and replacement. , 2007, Journal of theoretical biology.

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

[46]  M. Tomassini,et al.  Social Dilemmas and Cooperation in Complex Networks , 2006 .

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