Similarity-based cooperation and spatial segregation.

We analyze a cooperative game, where the cooperative act is not based on the previous behavior of the coplayer, but on the similarity between the players. This system has been studied in a mean-field description recently [Phys. Rev. E 68, 046129 (2003)]]. Here, the spatial extension to a two-dimensional lattice is studied, where each player interacts with eight players in a Moore neighborhood. The system shows a strong segregation independent of parameters. The introduction of a local conversion mechanism towards tolerance allows for four-state cycles and the emergence of spiral waves in the spatial game. In the case of asymmetric costs of cooperation a rich variety of complex behavior is observed depending on both cooperation costs. Finally, we study the stabilization of a cooperative fixed point of a forecast rule in the symmetric game, which corresponds to cooperation across segregation borders. This fixed point becomes unstable for high cooperation costs, but can be stabilized by a linear feedback mechanism.

[1]  G. Szabó,et al.  Cooperation for volunteering and partially random partnerships. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[2]  Gilbert Roberts,et al.  Behaviorial evolution: does similarity breed cooperation? , 2002, Nature.

[3]  M. Feldman,et al.  Local dispersal promotes biodiversity in a real-life game of rock–paper–scissors , 2002, Nature.

[4]  G. G. Stokes.  "J." , 1890, The New Yale Book of Quotations.

[5]  Arne Traulsen,et al.  Minimal model for tag-based cooperation. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[6]  O. D. Duncan,et al.  A METHODOLOGICAL ANALYSIS OF SEGREGATION INDEXES , 1955 .

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

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

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

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

[11]  Ross A. Hammond,et al.  The Evolution of Ethnocentric Behavior , 2003 .

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

[13]  M. Doebeli,et al.  Variable investment, the Continuous Prisoner's Dilemma, and the origin of cooperation , 1999, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[14]  W. Hamilton.  The Evolution of Altruistic Behavior , 1963, The American Naturalist.

[15]  S. Bornholdt,et al.  Coevolutionary games on networks. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

[18]  J. Neumann,et al.  Theory of games and economic behavior , 1945, 100 Years of Math Milestones.

[19]  D. Fudenberg,et al.  Emergence of cooperation and evolutionary stability in finite populations , 2004, Nature.

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

[21]  Petter Holme,et al.  Prisoners' dilemma in real-world acquaintance networks: spikes and quasiequilibria induced by the interplay between structure and dynamics. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[23]  M. Nowak,et al.  Evolutionary Dynamics of Biological Games , 2004, Science.

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

[25]  György Szabó,et al.  Phase transition and selection in a four-species cyclic predator-prey model. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[26]  M A Nowak,et al.  The dynamics of indirect reciprocity. , 1998, Journal of theoretical biology.

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

[28]  A V Herz,et al.  Collective phenomena in spatially extended evolutionary games. , 1994, Journal of theoretical biology.

[29]  Marcus Frean,et al.  Rock–scissors–paper and the survival of the weakest , 2001, Proceedings of the Royal Society of London. Series B: Biological Sciences.

[30]  K. Lindgren,et al.  Evolutionary dynamics of spatial games , 1994 .

[31]  Generalized mean-field study of a driven lattice gas. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[32]  Bonnie L Bassler,et al.  Chemical communication among bacteria , 2003, Proceedings of the National Academy of Sciences of the United States of America.

[33]  M A Nowak,et al.  Evolution: Tides of tolerance , 2001, Nature.

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

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

[36]  György Szabó,et al.  Phase transitions and volunteering in spatial public goods games. , 2002, Physical review letters.

[37]  Thomas C. Schelling,et al.  Dynamic models of segregation , 1971 .

[38]  G. Hardin,et al.  The Tragedy of the Commons , 1968, Green Planet Blues.