On evolutionarily stable strategies and replicator dynamics in asymmetric two-population games

We analyze the main dynamical properties of the evolutionarily stable strategy ESS for asymmetric two-population games of finite size in its corresponding replicator dynamics. We introduce a defnition of ESS for two-population asymmetric games and a method of symmetrizing such an asymmetric game. Then, we show that every strategy profile of the asymmetric game corresponds to a strategy in the symmetric game, and that every Nash equilibrium (NE) of the asymmetric game corresponds to a (symmetric) NE of the symmetric version game. So, we study (standard) replicator dynamics for the asymmetric game and define corresponding (non-standard) dynamics of the symmetric game.

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

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

[3]  R. Selten.  A note on evolutionarily stable strategies in asymmetric animal conflicts. , 1980, Journal of theoretical biology.

[4]  L. Samuelson,et al.  Evolutionary Stability in Asymmetric Games , 1992 .

[5]  Cressman.  Frequency-Dependent Stability for Two-Species Interactions , 1996, Theoretical population biology.

[6]  K. Schlag,et al.  Evolutionary Stability in Asymmetric Population Games , 1995 .

[7]  Z. Retchkiman,et al.  A Vector Lyapunov Approach to the Stability Problem for the n-Population Continuous Time Replicator Dynamics , 2007 .

[8]  Michael A. Fishman,et al.  Asymmetric evolutionary games with non-linear pure strategy payoffs , 2008, Games Econ. Behav..

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

[10]  Eric van Damme,et al.  Non-Cooperative Games , 2000 .

[11]  R. Cressman.  Evolutionary Dynamics and Extensive Form Games , 2003 .

[12]  Karl H. Schlag,et al.  On the evolutionary selection of sets of Nash equilibria , 2007, J. Econ. Theory.

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

[14]  Ross Cressman,et al.  The Stability Concept of Evolutionary Game Theory , 1992 .

[15]  I. Bomze.  Non-cooperative two-person games in biology: A classification , 1986 .

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

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

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

[19]  R. Cressman.  Uninvadability in N-species frequency models for resident-mutant systems with discrete or continuous time. , 2006, Theoretical population biology.