Calculus of Variations and Geometric Measure Theory

R. Ferreira - D. Gomes - X. Yang

Two-scale homogenization of a stationary mean-field game

created by ferreira on 23 May 2019



Inserted: 23 may 2019
Last Updated: 23 may 2019

Year: 2019

ArXiv: 1905.02046 PDF


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.