Mean Field Games Systems under Displacement Monotonicity

Mészáros, Alpár R.; Mou, Chenchen

Abstract

In this note we prove the uniqueness of solutions to a class of mean field games systems subject to possibly degenerate individual noise. Our results hold true for arbitrary long time horizons and for general nonseparable Hamiltonians that satisfy a so-called displacement mono-tonicity condition. This monotonicity condition that we propose for nonseparable Hamiltonians is sharper and more general than the one proposed in the work [W. Gangbo et al., Ann. Probab., 50 (2022), pp. 2178-2217]. The displacement monotonicity assumptions imposed on the data actually provide not only uniqueness, but also the existence and regularity of the solutions. Our analysis uses elementary arguments and does not rely on the well-posedness of the corresponding master equations.

Citation

Mészáros, A. R., & Mou, C. (2024). Mean Field Games Systems under Displacement Monotonicity. SIAM Journal on Mathematical Analysis, 56(1), 529-553. https://doi.org/10.1137/22m1534353

• Journal Article Type: Article
• Acceptance Date: Aug 22, 2023
• Online Publication Date: Jan 9, 2024
• Publication Date: Feb 1, 2024
• Deposit Date: Feb 8, 2024
• Publicly Available Date: Feb 14, 2024
• Journal: SIAM Journal on Mathematical Analysis
• Print ISSN: 0036-1410
• Electronic ISSN: 1095-7154
• Publisher: Society for Industrial and Applied Mathematics
• Peer Reviewed: Peer Reviewed
• Volume: 56
• Issue: 1
• Pages: 529-553
• DOI: https://doi.org/10.1137/22m1534353
• Keywords: Analysis; Optimal Control Theory; Mean Field Games
• Public URL: https://durham-repository.worktribe.com/output/2230331