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arXiv · 2403.05426

Hidden monotonicity and canonical transformations for mean field games and master equations

Mohit Bansil·Alpár R. Mészáros
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Abstract

In this paper we unveil novel monotonicity conditions applicable for Mean Field Games through the exploration of finite dimensional $canonical\ transformations$. Our findings contribute to establishing new global well-posedness results for the associated master equations, also in the case of potentially degenerate idiosyncratic noise. Additionally, we show that recent advancements in global well-posedness results, specifically those related to displacement semi-monotone and anti-monotone data, can be easily obtained as a consequence of our main results.

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Mohit Bansil, Alpár R. Mészáros. 2024-03-08. Hidden monotonicity and canonical transformations for mean field games and master equations. https://doi.org/10.1017/fms.2025.10130

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