Mean field game master equations with anti-monotonicity conditions

It is well known that the monotonicity condition, either in Lasry–Lions sense or in displacement sense, is crucial for the global well-posedness of mean field game master equations, as well as for the uniqueness of mean field equilibria and solutions to mean field game systems. In the literature, th...

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Bibliographic Details
Published inJournal of the European Mathematical Society : JEMS
Main Authors Mou, Chenchen, Zhang, Jianfeng
Format Journal Article
LanguageEnglish
Published 18.04.2024
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Summary:It is well known that the monotonicity condition, either in Lasry–Lions sense or in displacement sense, is crucial for the global well-posedness of mean field game master equations, as well as for the uniqueness of mean field equilibria and solutions to mean field game systems. In the literature, the monotonicity conditions are always taken in a fixed direction. In this paper, we propose a new type of monotonicity condition in the opposite direction, which we call the anti-monotonicity condition, and establish the global well-posedness for mean field game master equations with non-separable Hamiltonians. Our anti-monotonicity condition allows our data to violate both the Lasry–Lions monotonicity and the displacement monotonicity conditions.
ISSN:1435-9855
1435-9863
DOI:10.4171/jems/1455