Spatial Evolution of Automata in the Prisoner's Dilemma

Abstract We apply the idea of evolution to a spatial model. Prisoners’ dilemmas or coordination games are played repeatedly within neighbourhoods where players do not optimise but instead copy successful strategies. Discriminative behaviour of players is introduced representing strategies as small automata, which can be in different states against different neighbours. Extensive simulations show that cooperation persists even in a stochastic environment, that players do not always coordinate on risk dominant equilibria in 2×2 coordination games, and that success among surviving strategies may differ. We present two analytical models that help understanding of these phenomena.

[1]  M. Nowak,et al.  MORE SPATIAL GAMES , 1994 .

[2]  R. Rob,et al.  Learning, Mutation, and Long Run Equilibria in Games , 1993 .

[3]  Raimar Richers.  The theory of economic development , 1961 .

[4]  H. Hotelling.  Stability in Competition , 1929 .

[5]  Mark D. Smucker,et al.  Iterated Prisoner's Dilemma with Choice and Refusal of Partners: Evolutionary Results , 1995, ECAL.

[6]  R. Nelson.  Recent Evolutionary Theorizing about Economic Change , 2005, Technology, Institutions, and Economic Growth.

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

[8]  J. M. Smith,et al.  The Logic of Animal Conflict , 1973, Nature.

[9]  P. Taylor,et al.  Evolutionarily Stable Strategies and Game Dynamics , 1978 .

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

[11]  A. Shaked,et al.  Altruists, Egoists and Hooligans in a Local Interaction Model , 1996 .

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

[13]  Glenn Ellison.  Learning, Local Interaction, and Coordination , 1993 .

[14]  John C. Harsanyi,et al.  Общая теория выбора равновесия в играх / A General Theory of Equilibrium Selection in Games , 1989 .

[15]  E. Zeeman.  Dynamics of the evolution of animal conflicts , 1981 .

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

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

[18]  Stephen Wolfram,et al.  Universality and complexity in cellular automata , 1983 .

[19]  Stuart Roath,et al.  Scanning electron microscopy and the surface morphology of human lymphocytes , 1978, Nature.

[20]  H. Young,et al.  The Evolution of Conventions , 1993 .

[21]  B A Huberman,et al.  Evolutionary games and computer simulations. , 1993, Proceedings of the National Academy of Sciences of the United States of America.

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

[23]  J. M. Sakoda.  The checkerboard model of social interaction , 1971 .

[24]  O. Kirchkamp.  Asynchronous Evolution of Pairs - How spatial evolution leads to inequality , 1995 .