Evolutionary Stability in Asymmetric Population Games

We extend the notions of evolutionary stability and, for the first time, that of neutral stability to asymmetric games played between two populations. Stability with respect to simultaneous entry of a small proportion of mutants into both populations is considered. Allocations where neither mutant can ever spread are called neutrally stable. For bimatrix games, neutral stability in the asymmetric population game is found to be a weaker concept than neutral stability in the asymmetric contest. Moreover existence is guaranteed for 2 x 2 bimatrix games. Sets of neutrally stable strategy pairs such that for any pair of mutants not in the set at least one mutant is driven out are called evolutionary stable. Evolutionarily stable sets are shown to be equivalent to strict equilibrium sets. Additionally, uniformity considerations are investigated.