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 . We also present several nu- merical simulations which illustrate the applicability of our approach to compute Cournot-Nash equilibria.
Continuum of players; Cournot-Nash equilibria; optimal transport; best-reply iteration; congestion; non-symmetric interactions;
Adrien Blanchet, and Guillaume Carlier, “Remarks on existence and uniqueness of Cournot-Nash equilibria in the non-potential case”, Mathematics and Financial Economics, vol. 8, n. 4, September 2014, pp. 417–433.
TSE Working Paper, n. 14-491, May 2014