The evolution of Walrasian behavior in oligopolies
In this paper an oligopoly of at least two firms producing a homogeneous good is considered. Firms repeatedly play a Cournot game. The only information available to firms are all last periods production quantities and profits. Therefore classic game-theoretic considerations cannot be applied. A good strategy in this setting seems to be the imitation of the behavior of the most successful competitor (based on past data). The occurrence of new information and behavior is modelled by allowing firms to experiment. The evolutionary model considered in this paper is described by a Markov chain on an arbitrarily fixed set of feasible production quantities. It is proved that only (evolutionary) stable sets are selected by the unique invariant measure of the induced Markov chain as the probability of experimentations tends to zero. Moreover it is shown that stable singletons and symmetric Walrasian equilibria coincide in general and that Walrasian equilibria can be approximated by stable proper intervals.
scientific article; zbMATH DE number 1428353