Volume 26, 2020
|Number of page(s)||45|
|Published online||14 February 2020|
Two-scale homogenization of a stationary mean-field game*
King Abdullah University of Science and Technology (KAUST), CEMSE Division,
23955-6900, Saudi Arabia.
** Corresponding author: firstname.lastname@example.org
Accepted: 30 December 2019
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
© EDP Sciences, SMAI 2020
Current usage metrics show cumulative count of Article Views (full-text article views including HTML views, PDF and ePub downloads, according to the available data) and Abstracts Views on Vision4Press platform.
Data correspond to usage on the plateform after 2015. The current usage metrics is available 48-96 hours after online publication and is updated daily on week days.
Initial download of the metrics may take a while.