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

This article is devoted to various methods (optimal transport, fixed-point, ordi- nary 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, contrary to the variational framework of [3]. We also present several nu- merical simulations which illustrate the applicability of our approach to compute Cournot-Nash equilibria.