Working paper

Optimal Transport and Cournot-Nash Equilibria

Adrien Blanchet, and Guillaume Carlier


We study a class of games with a continuum of players for which Cournot-Nash equilibria can be obtained by the minimisation of some cost, related to optimal transport. This cost is not convex in the usual sense in general but it turns out to have hidden strict convexity properties in many relevant cases. This enables us to obtain new uniqueness results and a characterisation of equilibria in terms of some partial differential equations, a simple numerical scheme in dimension one as well as an analysis of the inefficiency of equilibria.


Cournot-Nash equilibria; mean-field games; optimal transport; externalities; Monge-Amp`ere equations; convexity along generalised geodesics;

Replaced by

Adrien Blanchet, and Guillaume Carlier, Optimal Transport and Cournot-Nash Equilibria, Mathematics of Operations Research, vol. 41, n. 1, July 16, 2015, pp. 125–145.

See also

Published in

TSE Working Paper, n. 12-321, June 2012