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arXiv · 2004.01660

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

Wilfrid Gangbo·Alpár R. Mészáros
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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 $\mathbb{R}^d$ and so, it is not compact.

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Wilfrid Gangbo, Alpár R. Mészáros. 2020-04-03. Global well-posedness of Master equations for deterministic displacement convex potential mean field games. https://arxiv.org/abs/2004.01660

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