Remarks on existence and uniqueness of Cournot-Nash equilibria in the non-potential case

TL;DR

This paper explores methods like optimal transport and fixed-point techniques to establish existence and uniqueness of Cournot-Nash equilibria in non-potential games with continuum players, including numerical simulations.

Contribution

It introduces new approaches for analyzing non-potential games with continuum players, focusing on existence and uniqueness of equilibria using various mathematical tools.

Findings

Methods successfully establish equilibrium existence.

Numerical simulations demonstrate practical computation.

Applicable to games with attractive and repulsive effects.

Abstract

This article is devoted to various methods (optimal transport, fixed-point, ordinary differential equations) to obtain existence and/or uniqueness of Cournot-Nash equilibria for games with a continuum of players with both attractive and repulsive effects. We mainly address separable situations but for which the game does not have a potential. We also present several numerical simulations which illustrate the applicability of our approach to compute Cournot-Nash equilibria.