The evolution of Walrasian behavior in oligopolies

Abstract

This paper studies an explicitly dynamic evolutionary model of Cournot oligopoly in which the behavior of firms is based on imitation of success and experimentation. It is proved that only (evolutionary) stable sets are selected by the unique invariant measure of the induced Markov chain as the probability of experimentation tends to zero. Evolutionary stability refers to a finite population set-up here. We show that stable singletons and symmetric Walrasian equilibria coincide in general. Furthermore, Walrasian equilibria can be approximated by stable proper intervals. These results generalize and extend the approach of Vega-Redondo [Vega-Redondo, F., 1997. The evolution of Walrasian behavior. Econometrica 65, 375–384].