Global well-posedness of Master equations for deterministic displacement convex potential mean field games

2020/04/03 by Wilfrid Gangbo, Alpár R. Mészáros, Gangbo, Wilfrid +1 · 9 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Functional Analysis (math.FA) #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2004.01660

openalex publication_date 2020/04/03 · openalex created_date 2023/02/11 · openalex updated_date 2026/07/28

Abstract

This manuscript constructs global in time solutions to the master equations for potential Mean Field Games. The study concerns a class of Lagrangians and initial data functions, which are displacement convex and so, it may be in dichotomy with the class of so--called monotone functions, 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 ℝ^d and so, it is not compact.

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• Guaranteeing Higher Order Convergence Rates for Accelerated Wasserstein Gradient Flow Schemes
• Particle system approximation of Nash equilibria in large games
• Quantitative convergence for displacement monotone Mean Field Games of control
• Iterative Schemes for Markov Perfect Equilibria
• Convergence of drift-diffusion PDEs arising as Wasserstein gradient flows of convex functions

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