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

Gangbo, Wilfrid; Mészáros, Alpár R.

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


Authors

Wilfrid Gangbo



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 Mar 28, 2024
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

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Published Journal Article (Early View) (659 Kb)
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Publisher Licence URL
http://creativecommons.org/licenses/by-nc-nd/4.0/

Copyright Statement
Early View © 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.






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