Global Well-Posedness of Displacement Monotone Degenerate Mean Field Games Master Equations

Bansil, Mohit; Mészáros, Alpár R.; Mou, Chenchen

Abstract

In this paper we construct global in time classical solutions to mean field game master equations in the lack of idiosyncratic noise in the individual agents’ dynamics. These include both deterministic models and dynamics driven solely by a Brownian common noise. We consider a general class of nonseparable Hamiltonians and final data functions that are supposed to be displacement monotone. Our main results unify and generalize in particular some of the well-posedness results on displacement monotone master equations obtained recently by Gangbo and Mészáros [Comm. Pure Appl. Math., 75 (2022), pp. 2685–2801] and Gangbo et al. [Ann. Probab., 50 (2022), pp. 2178–2217].

Citation

Bansil, M., Mészáros, A. R., & Mou, C. (2025). Global Well-Posedness of Displacement Monotone Degenerate Mean Field Games Master Equations. SIAM Journal on Control and Optimization, 63(2), 993-1021. https://doi.org/10.1137/23m1627651

• Journal Article Type: Article
• Acceptance Date: Nov 28, 2024
• Online Publication Date: Mar 31, 2025
• Publication Date: Apr 30, 2025
• Deposit Date: Apr 4, 2025
• Publicly Available Date: Apr 9, 2025
• Journal: SIAM Journal on Control and Optimization
• Print ISSN: 0363-0129
• Electronic ISSN: 1095-7138
• Publisher: Society for Industrial and Applied Mathematics
• Peer Reviewed: Peer Reviewed
• Volume: 63
• Issue: 2
• Pages: 993-1021
• DOI: https://doi.org/10.1137/23m1627651
• Public URL: https://durham-repository.worktribe.com/output/3775470