Evolutionary and asymptotic stability in symmetric multi-player games

Abstract.We provide a classification of symmetric three-player games with two strategies and investigate evolutionary and asymptotic stability (in the replicator dynamics) of their Nash equilibria. We discuss similarities and differences between two-player and multi-player games. In particular, we construct examples which exhibit a novel behavior not found in two-player games.

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

[2]  C Cannings,et al.  Multi-player matrix games. , 1997, Bulletin of mathematical biology.

[3]  William H. Sandholm,et al.  Potential Games with Continuous Player Sets , 2001, J. Econ. Theory.

[4]  L. Blume.  The Statistical Mechanics of Strategic Interaction , 1993 .

[5]  Chris Cannings,et al.  Models of animal conflict , 1976 .

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

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

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

[9]  Youngse Kim,et al.  Equilibrium Selection inn-Person Coordination Games , 1996 .

[10]  E. C. Zeeman,et al.  Population dynamics from game theory , 1980 .

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

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

[13]  L. Shapley,et al.  Potential Games , 1994 .

[14]  Glenn Ellison.  Basins of Attraction, Long-Run Stochastic Stability, and the Speed of Step-by-Step Evolution , 2000 .

[15]  Josef Hofbauer,et al.  A differential Game Approach to Evolutionary Equilibrium Selection , 2002, IGTR.

[16]  H. Peyton Young,et al.  Individual Strategy and Social Structure , 2020 .

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