Cournot Nash equilibria and Optimal Transport

Résumé

For a class of nonatomic games, we prove, by optimal transport techniques, various existence, uniqueness and variational characterization results for Nash-Cournot equilibria. For a wide class of payoffs, minimizers of some cost (related to optimal transport) are Nash-Cournot equilibria. This cost is not convex in the usual sense in general but it turns out to have hidden strict convexity properties in many relevant cases. This enables us to obtain new uniqueness results as well as a characterization of equilibria in terms of some PDE and a simple numerical scheme in dimension one.