Spatial social dilemmas: Dilution, mobility and grouping effects with imitation dynamics

We present an extensive, systematic study of the Prisoner’s Dilemma and Snowdrift games on a square lattice under a synchronous, noiseless imitation dynamics. We show that for both the occupancy of the network and the (random) mobility of the agents there are intermediate values that may increase the amount of cooperators in the system and new phases appear. We analytically determine the transition lines between these phases and compare with the mean field prediction and the observed behavior on a square lattice. We point out which are the more relevant microscopic processes that entitle cooperators to invade a population of defectors in the presence of mobility and discuss the universality of these results.

[1]  C. A. Aktipis,et al.  Is cooperation viable in mobile organisms? Simple Walk Away rule favors the evolution of cooperation in groups. , 2011, Evolution and human behavior : official journal of the Human Behavior and Evolution Society.

[2]  Ping-Ping Li,et al.  Cooperative behavior in evolutionary snowdrift games with the unconditional imitation rule on regular lattices. , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[3]  Attila Szolnoki,et al.  Ordering in spatial evolutionary games for pairwise collective strategy updates. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[5]  Wenjian Yu.  Mobility enhances cooperation in the presence of decision-making mistakes on complex networks. , 2011, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  Heinz Mühlenbein,et al.  Evolution of Cooperation in a Spatial Prisoner's Dilemma , 2002, Adv. Complex Syst..

[7]  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.

[8]  J. M. Oshorn.  Proc. Nat. Acad. Sei , 1978 .

[9]  Christoph Hauert,et al.  Effects of Space in 2 × 2 Games , 2002, Int. J. Bifurc. Chaos.

[10]  Anatol Rapoport,et al.  Two-person game theory , 1966 .

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

[12]  HanXin Yang,et al.  Universal role of migration in the evolution of cooperation , 2010, 1005.5453.

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

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

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

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

[17]  J. Koella,et al.  The spatial spread of altruism versus the evolutionary response of egoists , 2000, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[18]  Zhuo Chen,et al.  Evolution of cooperation among mobile agents , 2010, 1006.0772.

[19]  Shinsuke Suzuki,et al.  Oscillatory dynamics in the coevolution of cooperation and mobility. , 2011, Journal of theoretical biology.

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

[21]  R. Rosenfeld.  Nature , 2009, Otolaryngology--head and neck surgery : official journal of American Academy of Otolaryngology-Head and Neck Surgery.

[22]  C. Hauert.  Fundamental clusters in spatial 2×2 games , 2001, Proceedings of the Royal Society of London. Series B: Biological Sciences.

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

[24]  Jun Zhang,et al.  Evolution of cooperation among mobile agents with heterogenous view radii , 2011 .

[25]  Erwin Frey,et al.  Mobility, fitness collection, and the breakdown of cooperation. , 2013, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  M. Nowak,et al.  THE SPATIAL DILEMMAS OF EVOLUTION , 1993 .

[27]  L. Tian,et al.  Spatial evolutionary game with bond dilution , 2010 .

[28]  Guangming Xie,et al.  Different Reactions to Adverse Neighborhoods in Games of Cooperation , 2012, PloS one.

[29]  Hai Lin,et al.  Cooperation among mobile individuals with payoff expectations in the spatial prisoner's dilemma game , 2011 .

[30]  M H Vainstein,et al.  Disordered environments in spatial games. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[31]  M. Tomassini,et al.  Hawks and Doves on small-world networks. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

[32]  Ulf Dieckmann,et al.  Adaptive Evolution of Social Traits: Origin, Trajectories, and Correlations of Altruism and Mobility , 2004, The American Naturalist.

[33]  S. Számadó,et al.  The effect of dispersal and neighbourhood in games of cooperation. , 2008, Journal of theoretical biology.

[34]  Ángel Sánchez,et al.  Effect of spatial structure on the evolution of cooperation , 2008, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Richard E. Michod,et al.  The Evolution of Cooperation in Spatially Heterogeneous Populations , 1996, The American Naturalist.

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

[37]  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.

[38]  O. Leimar,et al.  The evolution of cooperation in mobile organisms , 1993, Animal Behaviour.

[39]  Zhi-Xi Wu,et al.  Promotion of cooperation by aspiration-induced migration , 2011 .

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

[41]  B. Wang,et al.  Role of aspiration-induced migration in cooperation. , 2010, Physical review. E, Statistical, nonlinear, and soft matter physics.

[42]  汪映海,et al.  Evolutionary snowdrift game with disordered environments in mobile societies , 2007 .

[43]  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.

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

[45]  Hongyan Cheng,et al.  Payoff-related migration enhances cooperation in the prisoner's dilemma game , 2011 .

[46]  L. Dugatkin,et al.  Rover: A Strategy for Exploiting Cooperators in a Patchy Environment , 1991, The American Naturalist.

[47]  C Athena Aktipis,et al.  Know when to walk away: contingent movement and the evolution of cooperation. , 2004, Journal of theoretical biology.

[48]  G. Szabó,et al.  Motion of influential players can support cooperation in Prisoner’s Dilemma , 2008, 0810.0367.

[49]  M. Taborsky,et al.  Contingent movement and cooperation evolve under generalized reciprocity , 2005, Proceedings of the Royal Society B: Biological Sciences.

[50]  Hongyan Cheng,et al.  Motion depending on the strategies of players enhances cooperation in a co-evolutionary prisoner's dilemma game , 2010 .