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

arXiv: https://arxiv.org/abs/2403.05426 · HTML: https://mlsanity.com/paper/2403.05426/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 8 Mar 2024.

## Built on by (most cited first, 1 of 1)

- [Convergence analysis of controlled particle systems arising in deep learning: from finite to infinite sample size](https://mlsanity.com/paper/2404.05185/) (2024)

## Abstract (arXiv)

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.