Working paper

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

Adrien Blanchet, and Guillaume Carlier

Abstract

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 [3]. We also present several nu- merical simulations which illustrate the applicability of our approach to compute Cournot-Nash equilibria.

Keywords

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

Replaced by

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.

Reference

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

See also

Published in

TSE Working Paper, n. 14-491, May 2014