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Weak solutions for first order mean field games with local coupling

Cardaliaguet, Pierre (2015), Weak solutions for first order mean field games with local coupling, in 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
External document link
https://arxiv.org/abs/1305.7015v1
Date
2015
Book title
Analysis and Geometry in Control Theory and its Applications
Book author
Piernicola Bettiol, Piermarco Cannarsa, Giovanni Colombo, Monica Motta, Franco Rampazzo
Publisher
Springer
Published in
Berlin Heidelberg
Paris
ISBN
978-3-319-06916-6
Pages
111-158
Publication identifier
Metadata
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Author(s)
Cardaliaguet, Pierre
Abstract (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.
Subjects / Keywords
game theory; variational methods; field game systems; Nash equilibrium