Cournot-Bayesian General Equilibrium: A Radon Measure Approach

Abstract

In this paper, we consider a Cournot duopoly, in which any firm does not know the marginal costs of production of the other player, as a Bayesian game. In our game, the marginal costs depend on two infinite continuous sets of states of the world. We shall study, before the general case, an intermediate case in which only one player, the second one, shows infinitely many types. Then, we shall generalize to the case in which both players show infinitely many types depending on the marginal costs, where the marginal costs are given by the nature and each actual marginal cost is known only by the respective player. We find, in both cases, the general Nash equilibrium.

Keywords

• Cournot duopoly
• game theory
• Nash–Cournot equilibrium
• marginal costs
• Bayesian games
• infinite dimensional strategy space
• probability measure
• Radon measures