Cournot-Bayesian General Equilibrium: A Radon Measure Approach

David Carfì,Alessia Donato

doi:10.3390/math7010010

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.

Highlights

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
The marginal costs depend on two infinite continuous sets of states of the world
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

Summary

Introduction

The marginal costs depend on two infinite continuous sets of states of the world. Before the general case, an intermediate case in which only one player, the second one, shows infinitely many types. 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

Methods

Results

Conclusion