| Issue |
ESAIM: COCV
Volume 26, 2020
|
|
|---|---|---|
| Article Number | 17 | |
| Number of page(s) | 45 | |
| DOI | https://doi.org/10.1051/cocv/2020002 | |
| Published online | 14 February 2020 | |
Two-scale homogenization of a stationary mean-field game*
King Abdullah University of Science and Technology (KAUST), CEMSE Division,
Thuwal
23955-6900, Saudi Arabia.
** Corresponding author: This email address is being protected from spambots. You need JavaScript enabled to view it.
Received:
9
July
2019
Accepted:
30
December
2019
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.
Mathematics Subject Classification: 91A13 / 35F21 / 35B27
Key words: Mean-field game / homogenization / two-scale convergence
The authors were supported by King Abdullah University of Science and Technology (KAUST) baseline funds and KAUST OSR-CRG2017-3452.
© EDP Sciences, SMAI 2020
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