Evolutionary Stability in Asymmetric Population Games¤

We extend the notions of evolutionary stability and neutral stability to asymmetric games played between two populations. Assuming that a single strategy is initially played in each population, we consider the simultaneous entry of small proportions of mutants into both populations. The originally played strategy pair is called neutrally stable if the mutants cannot spread. For bimatrix games, neutral stability in the asymmetric population game is found to be a weaker concept than neutral stability in the correponding asymmetric contest. A set of neutrally stable strategy pairs is called evolutionarily stable if for any incumbent strategy pair in the set and for any pair of mutants not in the set at least one mutant strategy is driven out. Evolutionarily stable sets are shown to be equivalent to strict equilibrium sets. Additionally, we study the uniformity of invasion barriers.