Weak solutions for first order mean field games with local coupling
Optimization and Control
2013-05-31 v1
Abstract
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 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.
Keywords
Cite
@article{arxiv.1305.7015,
title = {Weak solutions for first order mean field games with local coupling},
author = {Pierre Cardaliaguet},
journal= {arXiv preprint arXiv:1305.7015},
year = {2013}
}