TY - JOUR
T1 - Two-scale homogenization of a stationary mean-field game
AU - Ferreira, Rita
AU - Gomes, Diogo A.
AU - Yang, Xianjin
N1 - KAUST Repository Item: Exported on 2020-10-01
Acknowledged KAUST grant number(s): OSR-CRG2017-3452
Acknowledgements: The authors were supported by King Abdullah University of Science and Technology (KAUST) baseline funds and KAUST OSR-CRG2017-3452.
PY - 2020/2/14
Y1 - 2020/2/14
N2 - 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.
AB - 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.
UR - http://hdl.handle.net/10754/660832
UR - https://www.esaim-cocv.org/10.1051/cocv/2020002
U2 - 10.1051/cocv/2020002
DO - 10.1051/cocv/2020002
M3 - Article
SN - 1292-8119
VL - 26
SP - 17
JO - ESAIM: Control, Optimisation and Calculus of Variations
JF - ESAIM: Control, Optimisation and Calculus of Variations
ER -