Noncooperative Oligopoly in Markets with a Cobb-Douglas Continuum of Traders

Abstract

In this paper, we reconsider two models of noncooperative oligopoly in general equilibrium proposed by Busetto et al. ((2008), (2011)): a version of the Shapley's window model for mixed exchange economies a la Shitovitz and its reformulation a la Cournot-Walras. We introduce the assumption that preferences of the traders belonging to the atomless part are represented by Cobb-Douglas utility functions. This assumption permits us to prove the existence of a Cournot-Nash equilibrium of the Shapley's window model - called Cobb-Douglas-Cournot-Nash equilibrium - without introducing further assumptions on atoms' endowments and preferences previously used by Busetto et al. (2011). Then, we show that the set of the Cobb-Douglas-Cournot-Nash equilibrium allocations coincides with the set of the Cournot-Walras equilibrium allocations.