Article

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

Adrien Blanchet et Guillaume Carlier

Résumé

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.

Mots-clés

Continuum of players; Cournot-Nash equilibria; optimal transport; best-reply iteration; congestion; non-symmetric interactions;

Remplace

Adrien Blanchet et Guillaume Carlier, « Remarks on existence and uniqueness of Cournot-Nash equilibria in the non-potential case », TSE Working Paper, n° 14-491, mai 2014.

Référence

Adrien Blanchet et Guillaume Carlier, « Remarks on existence and uniqueness of Cournot-Nash equilibria in the non-potential case », Mathematics and Financial Economics, vol. 8, n° 4, septembre 2014, p. 417–433.

Voir aussi

Publié dans

Mathematics and Financial Economics, vol. 8, n° 4, septembre 2014, p. 417–433