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

2016/02/26 by Annalisa Cesaroni, Cesaroni, Annalisa, Nicolas Dirr +3 · 1 citation
Computer Science · Economics, Econometrics and Finance · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Nonlinear Partial Differential Equations #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1602.08520

openalex publication_date 2016/02/26 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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

Cited by

• Fast and slow mean-field games

Related

• An ergodic problem for Mean Field Games: qualitative properties and numerical simulations
• Two-scale homogenization of a stationary mean-field game
• Homogenization of the backward-forward mean-field games systems in periodic environments
• Asymptotic Analysis of Mean Field Games with Small Common Noise
• Short time solution to the master equation of a first order mean field game system