Two-scale homogenization of a stationary mean-field game

2019/05/06 by Rita Ferreira, Ferreira, Rita, Diogo Gomes +3 · 1 citation
Mathematics · #35B27 #35F21 #65M22 #Analysis of PDEs (math.AP) #FOS: Mathematics #math.AP #msc:35B27 #msc:35F21 #msc:65M22

paper · pdf · doi:10.48550/arxiv.1905.02046

36 pages

arxiv created 2019/05/06 · arxiv updated 2019/05/07

Abstract

In this paper, we characterize the asymptotic behavior of a first-order stationary mean-field game (MFG) with a logarithm coupling, a quadratic Hamiltonian, and a periodically oscillating potential. This study falls into the realm of the homogenization theory, and our main tool is the two-scale convergence. Using this convergence, we rigorously derive the two-scale homogenized and the homogenized MFG problems, which encode the so-called macroscopic or effective behavior of the original oscillating MFG. Moreover, we prove existence and uniqueness of the solution to these limit problems.

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