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.
Publié le : 2015-02-02
Classification:
non-symmetric interactions,
Continuum of players,
best-reply iteration,
congestion,
optimal transport,
Cournot-Nash equilibria,
[MATH.MATH-AP]Mathematics [math]/Analysis of PDEs [math.AP]
@article{hal-01112228,
author = {Carlier, Guillaume and Blanchet, Adrien},
title = {Remarks on existence and uniqueness of Cournot-Nash equilibria in the non-potential case},
journal = {HAL},
volume = {2015},
number = {0},
year = {2015},
language = {en},
url = {http://dml.mathdoc.fr/item/hal-01112228}
}
Carlier, Guillaume; Blanchet, Adrien. Remarks on existence and uniqueness of Cournot-Nash equilibria in the non-potential case. HAL, Tome 2015 (2015) no. 0, . http://gdmltest.u-ga.fr/item/hal-01112228/