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.
Publié le : 2015-07-16
Classification:
Monge-Amp\ère equations,
convexity along generalised geodesics,
externalities,
mean-field games,
Cournot-Nash equilibria,
optimal transport,
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP],
[SHS.ECO]Humanities and Social Sciences/Economies and finances
@article{hal-00712488,
author = {Blanchet, Adrien and Carlier, Guillaume},
title = {Optimal transport and Cournot-Nash equilibria},
journal = {HAL},
volume = {2015},
number = {0},
year = {2015},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-00712488}
}
Blanchet, Adrien; Carlier, Guillaume. Optimal transport and Cournot-Nash equilibria. HAL, Tome 2015 (2015) no. 0, . http://gdmltest.u-ga.fr/item/hal-00712488/