Homogenization of a mean field game system in the small noise limit

Abstract

This paper concerns the simultaneous effect of homogenization and of the small noise limit for a $2^{\text{nd}}$ order mean field games (MFG) system with local coupling and quadratic Hamiltonian. We show under some additional assumptions that the solutions of our system converge to a solution of an effective $1^{\text{st}}$ order system whose effective operators are defined through a cell problem which is a $2^{\text{nd}}$ order system of ergodic MFG type. We provide several properties of the effective operators and we show that in general the effective system looses the MFG structure.

Corrected version, we eliminate a Proposition (7.5) which was false, without affecting the final result

References in corpus (1)

• On weak convergence of locally periodic functions