Evolutionary stability and Nash equilibrium in finite populations, with an application to price competition

Schaffer [Schaffer, M.E., 1988. Evolutionarily stable strategies for a finite population and a variable contest size. Journal of Theoretical Biololgy 132, 469-478] proposed a concept of evolutionary stability for finite-population models that has interesting implications in economic models of evolutionary learning, since it is related to perfectly competitive equilibrium. The present paper explores the relation of this concept to Nash equilibrium in particular classes of games, including constant-sum games, games with weak payoff externalities, and games where imitative decision rules are individually improving. An illustration of the latter is provided in the context of Bertrand oligopoly with homogeneous product which allows for a characterization of the set of evolutionarily stable prices.