Finite Population Dynamics and Mixed Equilibria

Abstract

This paper examines the stability of mixed-strategy Nash equilibria of symmetric games, viewed as population profiles in dynamical systems with learning within a single, finite population. Alternative models of imitation and myopic best reply are considered under different assumptions on the speed of adjustment. It is found that two specific refinements of mixed Nash equilibria identify focal rest points of these dynamics in general games. The relationship between both concepts is studied. In the 2×2 case, both imitation and myopic best reply yield strong stability results for the same type of mixed Nash equilibria.