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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DOI : 10.1051/cocv/2020002
Keywords: Mean-field game, homogenization, two-scale convergence
@article{COCV_2020__26_1_A17_0,
author = {Ferreira, Rita and Gomes, Diogo and Yang, Xianjin},
title = {Two-scale homogenization of a stationary mean-field game},
journal = {ESAIM: Control, Optimisation and Calculus of Variations},
year = {2020},
publisher = {EDP Sciences},
volume = {26},
doi = {10.1051/cocv/2020002},
mrnumber = {4064478},
zbl = {1437.91054},
language = {en},
url = {https://www.numdam.org/articles/10.1051/cocv/2020002/}
}
TY - JOUR AU - Ferreira, Rita AU - Gomes, Diogo AU - Yang, Xianjin TI - Two-scale homogenization of a stationary mean-field game JO - ESAIM: Control, Optimisation and Calculus of Variations PY - 2020 VL - 26 PB - EDP Sciences UR - https://www.numdam.org/articles/10.1051/cocv/2020002/ DO - 10.1051/cocv/2020002 LA - en ID - COCV_2020__26_1_A17_0 ER -
%0 Journal Article %A Ferreira, Rita %A Gomes, Diogo %A Yang, Xianjin %T Two-scale homogenization of a stationary mean-field game %J ESAIM: Control, Optimisation and Calculus of Variations %D 2020 %V 26 %I EDP Sciences %U https://www.numdam.org/articles/10.1051/cocv/2020002/ %R 10.1051/cocv/2020002 %G en %F COCV_2020__26_1_A17_0
Ferreira, Rita; Gomes, Diogo; Yang, Xianjin. Two-scale homogenization of a stationary mean-field game. ESAIM: Control, Optimisation and Calculus of Variations, Tome 26 (2020), article no. 17. doi: 10.1051/cocv/2020002
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The authors were supported by King Abdullah University of Science and Technology (KAUST) baseline funds and KAUST OSR-CRG2017-3452.
