English

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 ϵ\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.

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}
}
R2 v1 2026-06-22T00:25:00.740Z