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

Carlier, Guillaume; Blanchet, Adrien

Carlier, Guillaume; Blanchet, Adrien (2014), Remarks on existence and uniqueness of Cournot-Nash equilibria in the non-potential case, Mathematics and Financial Economics, 8, 4, p. 417-433. http://dx.doi.org/10.1007/s11579-014-0127-z

Type

Article accepté pour publication ou publié

External document link

http://hal.archives-ouvertes.fr/hal-00987753

Date

2014

Journal name

Mathematics and Financial Economics

Volume

Number

Publisher

Springer

Pages

417-433

Abstract (EN)

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.

Subjects / Keywords

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