Abstract
In this paper, we focus on stationary (ergodic) mean-field games (MFGs). These games arise in the study of the long-time behavior of finite-horizon MFGs. Motivated by a prior scheme for Hamilton–Jacobi equations introduced in Aubry–Mather's theory, we introduce a discrete approximation to stationary MFGs. Relying on Kakutani's fixed-point theorem, we prove the existence and uniqueness (up to additive constant) of solutions to the discrete problem. Moreover, we show that the solutions to the discrete problem converge, uniformly in the nonlocal case and weakly in the local case, to the classical solutions of the stationary problem.
Original language | English (US) |
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Journal | Journal of Dynamics and Games |
DOIs | |
State | Published - 2022 |
Bibliographical note
KAUST Repository Item: Exported on 2022-10-04Acknowledged KAUST grant number(s): OSR-CRG2021-4
Acknowledgements: The first and the second authors are supported by King Abdullah University of Science and Technology (KAUST) baseline funds and KAUST OSR-CRG2021-4