Optimal transport and Cournot-Nash equilibria

TL;DR

This paper explores a class of continuum-player games linked to optimal transport, revealing hidden convexity properties that lead to new uniqueness results, equilibrium characterizations via PDEs, and insights into equilibrium inefficiency.

Contribution

It introduces a novel approach connecting Cournot-Nash equilibria with optimal transport, uncovering hidden convexity and providing new analytical and numerical tools.

Findings

Hidden convexity properties enable uniqueness results

Equilibria characterized by partial differential equations

Analysis of the inefficiency of equilibria

Abstract

We study a class of games with a continuum of players for which Cournot-Nash equilibria can be obtained by the minimisation of some cost, related to optimal transport. 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 and a characterisation of equilibria in terms of some partial differential equations, a simple numerical scheme in dimension one as well as an analysis of the inefficiency of equilibria.