Weak KAM theory for potential MFG
Analysis of PDEs
2019-07-08 v2 Dynamical Systems
Abstract
We develop the counterpart of weak KAM theory for potential mean field games. This allows to describe the long time behavior of time-dependent potential mean field game systems. Our main result is the existence of a limit, as time tends to infinity, of the value function of an optimal control problem stated in the space of measures. In addition, we show a mean field limit for the ergodic constant associated with the corresponding Hamilton-Jacobi equation.
Keywords
Cite
@article{arxiv.1904.13287,
title = {Weak KAM theory for potential MFG},
author = {Pierre Cardaliaguet and Marco Masoero},
journal= {arXiv preprint arXiv:1904.13287},
year = {2019}
}