Noncooperative Oligopoly in Markets with a Continuum of Traders

In this paper, we study three prototypical models of noncooper- ative oligopoly in markets with a continuum of traders: the model of Cournot-Walras equilibrium of Codognato and Gabszewicz (1991), the model of Cournot-Nash equilibrium of Lloyd S. Shapley, and the model of Cournot-Walras equilibrium of Busetto et al. (2008). We argue that these models are all distinct and only the Shapley's model with a continuum of traders and atoms gives an endogenous explana- tion of the perfectly and imperfectly competitive behavior of agents in a one-stage setting. For this model, we prove a theorem of existence of a Cournot-Nash equilibrium.