Existence and optimality of Coumot-Nash equilibria in a bilateral oligopoly with atoms and an atomless part

摘要

We consider a bilateral oligopoly version of the Shapley window model with large traders, represented as atoms, and small traders, represented by an atomless part. For this model, we provide a general existence proof of a Cournot-Nash equilibrium that allows one of the two commodities to be held only by atoms. Then, we show, using a corollary proved by Shitovitz (Econometrica 41:467-501, 1973), that a Cournot-Nash allocation is Pareto optimal if and only if it is a Walras allocation.