Evolutionary Stability in Asymmetric Oligopoly

Abstract

It is a very well-known result that in terms of evolutionary stability the long-run outcome of a Cournot oligopoly market with fi nitely many fi rms approaches the perfectly competitive Walrasian market outcome (Vega-Redondo, 1997). However, in this paper we show that an asymmetric structure in the cost functions of fi rms may change the long-run outcome. Contrary to Tanaka (1999) we show that the evolutionarily stable price in an asymmetric Cournot oligopoly needs not equal the marginal cost, it may rather equal a weighted average of (diff erent) marginal cost. We apply a symmetrization technique in order to transform the game with asymmetric fi rms into a symmetric oligopoly game and then extend Schaff er’s defi nition (1988) of a fi nite population ESS (FPESS) to this setup. Moreover, we show that the FPESS in this game represents a stochastically stable state of an evolutionary process of imitation with experimentation.