Evolutionarily rational mutations in structured populations

Abstract

This paper considers an evolutionary dynamic to study games played in large populations that consist of many identical, potentially small subpopulations, where individuals interact with others in their subpopulation, rarely moving between them.Since long-run behavior depends on the used mutation strategies, a criterion loosely inspired by Maynard Smith's (1972) notion of an evolutionary stable strategy is imposed on mutation strategies – we ask which mutation strategies are robust to “invasions” by others. Non-degenerate mutation strategies lead to behavioral diversity. Populations that use different interaction strategies in different subpopulations can be robust to “invasions,” even if each interaction strategy would not be robust if used by the entire population.Mutation strategies satisfying the proposed criterion always exist. A simple characterization is possible for the case of weak selection. The developed theory yields a rich class of predictions that can be inconsistent with standard concepts like Nash equilibrium. For instance, for finitely repeated games, the model always predicts relatively high payoffs if the stage game is repeated sufficiently often.