Global Well‐Posedness of Master Equations for Deterministic Displacement Convex Potential Mean Field Games

Gangbo, Wilfrid; Mészáros, Alpár R.

Abstract

This manuscript constructs global in time solutions to master equations for potential mean field games. The study concerns a class of Lagrangians and initial data functions that are displacement convex, and so this property may be in dichotomy with the so-called Lasry–Lions monotonicity, widely considered in the literature. We construct solutions to both the scalar and vectorial master equations in potential mean field games, when the underlying space is the whole space Rd , and so it is not compact.

Citation

Gangbo, W., & Mészáros, A. R. (2022). Global Well‐Posedness of Master Equations for Deterministic Displacement Convex Potential Mean Field Games. Communications on Pure and Applied Mathematics, 75(12), 2685-2801. https://doi.org/10.1002/cpa.22069

• Journal Article Type: Article
• Online Publication Date: Jun 15, 2022
• Publication Date: 2022-12
• Deposit Date: Jun 16, 2022
• Publicly Available Date: Jun 20, 2022
• Journal: Communications on Pure and Applied Mathematics
• Print ISSN: 0010-3640
• Electronic ISSN: 1097-0312
• Publisher: Wiley
• Peer Reviewed: Peer Reviewed
• Volume: 75
• Issue: 12
• Pages: 2685-2801
• DOI: https://doi.org/10.1002/cpa.22069
• Public URL: https://durham-repository.worktribe.com/output/1201612