Evolution of Cooperation in a Spatial Prisoner's Dilemma

We investigate the spatial distribution and the global frequency of agents who can either cooperate or defect. The agent interaction is described by a deterministic, non-iterated prisoner's dilemma game, further each agent only locally interacts with his neighbors. Based on a detailed analysis of the local payoff structures we derive critical conditions for the invasion or the spatial coexistence of cooperators and defectors. These results are concluded in a phase diagram that allows us to identify five regimes, each characterized by a distinct spatiotemporal dynamics and a corresponding final spatial structure. In addition to the complete invasion of defectors, we find coexistence regimes with either a majority of cooperators in large spatial domains, or a minority of cooperators organized in small non-stationary domains or in small clusters. The analysis further allowed a verification of computer simulation results by Nowak and May (1993). Eventually, we present simulation results of a true 5-person game on a lattice. This modification leads to non-uniform spatial interactions that may even enhance the effect of cooperation.

[1]  M. Olson,et al.  The Logic of Collective Action: Public Goods and the Theory of Groups. , 1973 .

[2]  L A Dugatkin,et al.  N-person games and the evolution of co-operation: a model based on predator inspection in fish. , 1990, Journal of theoretical biology.

[3]  A. Rapoport,et al.  Prisoner's Dilemma , 1965 .

[4]  Heinz Mühlenbein,et al.  Frequency Dependent Invasion in a Spatial Environment , 2003 .

[5]  B. Huberman,et al.  The outbreak of cooperation , 1993 .

[6]  M Matsushima,et al.  Evolution of strategies in the three-person iterated prisoner's dilemma game. , 1998, Journal of theoretical biology.

[7]  Heinz Mühlenbein,et al.  Coordination of Decisions in a Spatial Agent Model , 2001, ArXiv.

[8]  Mats G. Nordahl,et al.  Cooperation and Community Structure in Artificial Ecosystems , 1993, Artificial Life.

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

[10]  M. Oliphant.  Evolving cooperation in the non-iterated prisoner''s dilemma , 1994 .

[11]  Heinz Mühlenbein,et al.  Stochastic Analysis of Cellular Automata with Application to the Voter Model , 2002, Adv. Complex Syst..

[12]  R. Boyd.  Mistakes allow evolutionary stability in the repeated prisoner's dilemma game. , 1989, Journal of theoretical biology.

[13]  David P. Kraines,et al.  Learning to cooperate with Pavlov an adaptive strategy for the iterated Prisoner's Dilemma with noise , 1993 .

[14]  G. Hardin,et al.  Tragedy of the Commons , 1968 .

[15]  Vladimir Akimov,et al.  Automata Simulation of N-Person Social Dilemma Games , 1994 .

[16]  Roger Ware,et al.  Evolutionary stability in the repeated prisoner's dilemma , 1989 .

[17]  Eizo Akiyama,et al.  Evolution of Cooperation, Differentiation, Complexity, and Diversity in an Iterated Three-Person Game , 1995, Artificial Life.

[18]  M N,et al.  The Evolution of Cooperation in a Lattice-Structured Population , 1996 .

[19]  David B. Fogel,et al.  On the Relationship between the Duration of an Encounter and the Evolution of Cooperation in the Iterated Prisoner's Dilemma , 1995, Evolutionary Computation.

[20]  P. Grim.  The undecidability of the spatialized prisoner's dilemma , 1997 .

[21]  Heinz Mühlenbein,et al.  Darwin's Continent Cycle Theory and Its Simulation by the Prisoner's Dilemma , 1991, Complex Syst..

[22]  R. Trivers.  The Evolution of Reciprocal Altruism , 1971, The Quarterly Review of Biology.

[23]  Kristian Lindgrena,et al.  Coevolution of strategies in n-person Prisoner ' s Dilemma , 2000 .

[24]  Xin Yao,et al.  Co-Evolution in Iterated Prisoner's Dilemma with Intermediate Levels of Cooperation: Application to Missile Defense , 2002, Int. J. Comput. Intell. Appl..

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

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

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

[28]  M. Doebeli,et al.  Population dynamics, demographic stochasticity, and the evolution of cooperation. , 1997, Proceedings of the National Academy of Sciences of the United States of America.

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

[30]  J. Lorberbaum,et al.  No strategy is evolutionarily stable in the repeated prisoner's dilemma. , 1994, Journal of theoretical biology.

[31]  Andrew M. Colman,et al.  The complexity of cooperation: Agent-based models of competition and collaboration , 1998, Complex..

[32]  M. Macy.  Natural Selection and Social Learning in Prisoner's Dilemma , 1996 .

[33]  Rick Durrett,et al.  Stochastic Spatial Models , 1999, SIAM Rev..

[34]  Xin Yao,et al.  An Experimental Study of N-Person Iterated Prisoner's Dilemma Games , 1993, Informatica.

[35]  Sidney C. Sufrin,et al.  The Logic of Collective Action: Public Goods and the Theory of Groups. , 1966 .

[36]  A. Rapoport.  Prisoner's Dilemma: Reflections and Recollections , 1995 .

[37]  R. Boyd,et al.  No pure strategy is evolutionarily stable in the repeated Prisoner's Dilemma game , 1987, Nature.

[38]  W. Hamilton,et al.  The evolution of cooperation. , 1984, Science.

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

[40]  Robert Hoffmann,et al.  Twenty Years on: The Evolution of Cooperation Revisited , 2000, J. Artif. Soc. Soc. Simul..

[41]  M. Nowak,et al.  The Alternating Prisoner's Dilemma , 1994 .

[42]  S. L. Lima,et al.  Iterated Prisoner's Dilemma: An Approach to Evolutionarily Stable Cooperation , 1989, The American Naturalist.

[43]  Frank Schweitzer,et al.  Modeling complexity in economic and social systems , 2002 .

[44]  Oliver Kirchkamp,et al.  Spatial Evolution of Automata in the Prisoner's Dilemma , 2000, Social Science Microsimulation.

[45]  B. Huberman,et al.  THE DYNAMICS OF SOCIAL DILEMMAS , 1994 .