Calculus of Variations and Geometric Measure Theory

A. Cesaroni - N. Dirr - C. Marchi

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

created by cesaroni on 27 Feb 2016
modified on 09 Mar 2024


Published Paper

Inserted: 27 feb 2016
Last Updated: 9 mar 2024

Journal: SIAM J. Math. Anal.
Volume: 48
Number: 4
Pages: 2701-2729
Year: 2016


This paper concerns the simultaneous effect of homogenization and of the small noise limit for a 2nd 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 1st order system whose effective operators are defined through a cell problem which is a 2nd 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.