Equilibrium selection in evolutionary games with random matching of players.

We discuss stochastic dynamics of populations of individuals playing games. Our models possess two evolutionarily stable strategies: an efficient one, where a population is in a state with the maximal payoff (fitness) and a risk-dominant one, where players are averse to risks. We assume that individuals play with randomly chosen opponents (they do not play against average strategies as in the standard replicator dynamics). We show that the long-run behavior of a population depends on its size and the mutation level.

[1]  M. Freidlin,et al.  Random Perturbations of Dynamical Systems , 1984 .

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

[3]  L. Samuelson.  Evolutionary Games and Equilibrium Selection , 1997 .

[4]  K Sigmund,et al.  A note on evolutionary stable strategies and game dynamics. , 1979, Journal of theoretical biology.

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

[6]  F. Vega-Redondo,et al.  Efficient Equilibrium Selection in Evolutionary Games with Random Matching , 1996 .

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

[8]  Jacek Miekisz,et al.  Statistical mechanics of spatial evolutionary games , 2002, cond-mat/0210094.

[9]  Fernando Vega-Redondo,et al.  Evolution, Games, and Economic Behaviour , 1996 .

[10]  Jacek Miekisz,et al.  Stochastic stability in spatial three-player games , 2004, cond-mat/0409649.

[11]  Jörgen W. Weibull,et al.  Evolutionary Game Theory , 1996 .

[12]  J. M. Smith.  The theory of games and the evolution of animal conflicts. , 1974, Journal of theoretical biology.

[13]  H. Peyton Young,et al.  Stochastic Evolutionary Game Dynamics , 1990 .

[14]  Josef Hofbauer,et al.  The theory of evolution and dynamical systems , 1988 .

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

[16]  M. Freidlin,et al.  ON SMALL RANDOM PERTURBATIONS OF DYNAMICAL SYSTEMS , 1970 .

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