Homogenization of a stationary mean-field game via two-scale convergence

Rita Ferreira
King Abdullah Univ. of Science and Technology (KAUST)

In this talk, we address the study of 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.

This is a joint work with Diogo Gomes (KAUST) and Xianjin Yang (KAUST).

Presentation (PDF File)

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