Optimal transport and Cournot-Nash equilibria

Blanchet, Adrien; Carlier, Guillaume

Blanchet, Adrien; Carlier, Guillaume (2016), Optimal transport and Cournot-Nash equilibria, Mathematics of Operations Research, 41, 3, p. 125-145. 10.1287/moor.2015.0719

Type

Article accepté pour publication ou publié

External document link

https://arxiv.org/abs/1206.6571v1

Date

2016

Journal name

Mathematics of Operations Research

Volume

Number

Publisher

Institute of Management Sciences

Published in

Paris

Pages

125-145

Abstract (EN)

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.

Subjects / Keywords

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