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

Adrien Blanchet (1) , Guillaume Carlier (2, 3)

1 GREMAQ - Groupe de recherche en économie mathématique et quantitative
2 MOKAPLAN - Méthodes numériques pour le problème de Monge-Kantorovich et Applications en sciences sociales
3 CEREMADE - CEntre de REcherches en MAthématiques de la DEcision

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.

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

Domaines: Optimisation et contrôle [math.OC]

Adrien Blanchet, Guillaume Carlier. Remarks on existence and uniqueness of Cournot-Nash equilibria in the non-potential case. 2014. ⟨hal-00987753⟩