Finite-Population "Mass-Action" and Evolutionary Stability

Nash proposed an interpretation of mixed strategies as the average pure-strategy play of a population of players randomly matched to play a normal-form game. If populations are finite, some equilibria of the underlying game have no such corresponding “mass-action” equilibrium. We show that for mixed strategy equilibria of 2 × 2 games, the requirement of such a correspondence is equivalent to neutral evolutionary stability.