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

Gangbo, Wilfrid and Mészáros, Alpár R. (2022) 'Global Well‐Posedness of Master Equations for Deterministic Displacement Convex Potential Mean Field Games.', Communications on Pure and Applied Mathematics .

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.

Item Type:Article
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Status:Peer-reviewed
Publisher Web site:https://doi.org/10.1002/cpa.22069
Publisher statement:© 2022 The Authors. Communications on Pure and Applied Mathematics published by Wiley Periodicals LLC. This is an open access article under the terms of the Creative Commons Attribution-NonCommercial-NoDerivs License, which permits use and distribution in any medium, provided the original work is properly cited, the use is non-commercial and no modifications or adaptations are made.
Date accepted:No date available
Date deposited:20 June 2022
Date of first online publication:15 June 2022
Date first made open access:20 June 2022

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