KAUST DepartmentComputer, Electrical and Mathematical Sciences and Engineering (CEMSE) Division
Applied Mathematics and Computational Science Program
KAUST Grant NumberOSR-CRG2017-3452
Preprint Posting Date2019-05-06
Online Publication Date2020-02-14
Print Publication Date2020
Permanent link to this recordhttp://hdl.handle.net/10754/660832
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AbstractIn 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.
CitationFerreira, R., Gomes, D., & Yang, X. (2020). Two-scale homogenization of a stationary mean-field game. ESAIM: Control, Optimisation and Calculus of Variations, 26, 17. doi:10.1051/cocv/2020002
SponsorsThe authors were supported by King Abdullah University of Science and Technology (KAUST) baseline funds and KAUST OSR-CRG2017-3452.