Evolutionary Stability Against Multiple Mutations

It is known (see, e.g., Weibull, 1995) that an evolutionarily stable strategy is not necessarily robust against multiple mutations. Precise definition and analysis of ‘evolutionarily stable strategy against multiple mutations’ are not available in the literature. In this article, we formalize evolutionarily robustness against multiple mutations. Our main result shows that such a robust strategy is necessarily a pure strategy. Further, we study some equivalent formulations and properties of evolutionary stability against multiple mutations. In particular, we characterize completely the robustness against multiple mutations in 2×2 games.