Evolutionary Stability in Asymmetric Games *

We examine dynamic models of evolutionary selection processes on asymmetric two-player games. Conditions are established under which dynamic selection processes will yield outcomes that respect iterated strict dominance. The addition of a stability requirement ensures that outcomes will be Nash equilibria. However, we find that stable outcomes need not respect weak dominance, and hence need not yield perfect equilibria. We conclude that evolutionary arguments readily motivate such equilibrium oncepts as rationalizability and Nash equilibrium, but appear to provide little basis for even such simple refinements of Nash equilibrium as the recommendation that dominated strategies not be played. Journal of Economic Literafure Classification Numbers: C70, C72.