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, 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. 
Adrien Blanchet (GREMAQ), Guillaume Carlier (CEREMADE)
math.OC