Weak solutions for first order mean field games with local coupling

Cardaliaguet, Pierre

Cardaliaguet, Pierre (2015), Weak solutions for first order mean field games with local coupling, dans Piernicola Bettiol, Piermarco Cannarsa, Giovanni Colombo, Monica Motta, Franco Rampazzo, Analysis and Geometry in Control Theory and its Applications, Springer : Berlin Heidelberg, p. 111-158. 10.1007/978-3-319-06917-3_5

Type

Chapitre d'ouvrage

Lien vers un document non conservé dans cette base

https://arxiv.org/abs/1305.7015v1

Date

2015

Titre de l'ouvrage

Analysis and Geometry in Control Theory and its Applications

Auteurs de l’ouvrage

Piernicola Bettiol, Piermarco Cannarsa, Giovanni Colombo, Monica Motta, Franco Rampazzo

Éditeur

Springer

Ville d’édition

Berlin Heidelberg

Paris

Isbn

978-3-319-06916-6

Pages

111-158

Résumé (EN)

Existence and uniqueness of a weak solution for first order mean field game systems with local coupling are obtained by variational methods. This solution can be used to devise $\epsilon-$Nash equilibria for deterministic differential games with a finite (but large) number of players. For smooth data, the first component of the weak solution of the MFG system is proved to satisfy (in a viscosity sense) a time-space degenerate elliptic differential equation.

Mots-clés

game theory; variational methods; field game systems; Nash equilibrium