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, contrary to the variational framework of Blanchet and Carlier (Optimal transport and Cournot–Nash equilibria, 2012). We also present several numerical 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.
Mathematics and Financial Economics, vol. 8, n. 4, September 2014, pp. 417–433