Evolutionarily Stable Strategies and Replicator Dynamics in Asymmetric Two-Population Games

We analyze the main dynamical properties of the evolutionarily stable strategy (ℰ) for asymmetric two-population games of finite size and its corresponding replicator dynamics. We introduce a definition of ℰ for two-population asymmetric games and a method of symmetrizing such an asymmetric game. We show that every strategy profile of the asymmetric game corresponds to a strategy in the symmetric game, and that every Nash equilibrium (ℰ) of the asymmetric game corresponds to a (symmetric) ℰ of the symmetric version game. We study the (standard) replicator dynamics for the asymmetric game and we define the corresponding (non-standard) dynamics of the symmetric game. We claim that the relationship between ℰ, ℰ and the stationary states () of the dynamical system for the asymmetric game can be studied by analyzing the dynamics of the symmetric game.