# Mean Field Games Master Equations with Non-separable Hamiltonians and Displacement Monotonicity

arXiv: https://arxiv.org/abs/2101.12362 · HTML: https://mlsanity.com/paper/2101.12362/

## Key facts

- Cited by 4 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 29 Jan 2021.

## Built on by (most cited first, 4 of 4)

- [Unified continuous-time q-learning for mean-field game and mean-field control problems](https://mlsanity.com/paper/2407.04521/) (2024)
- [Score-based Neural Ordinary Differential Equations for Computing Mean Field Control Problems](https://mlsanity.com/paper/2409.16471/) (2024)
- [Convergence analysis of controlled particle systems arising in deep learning: from finite to infinite sample size](https://mlsanity.com/paper/2404.05185/) (2024)
- [Nesterov acceleration in optimizing over probability measures](https://mlsanity.com/paper/2607.23008/) (2026)

## Abstract (arXiv)

In this manuscript, we propose a structural condition on non-separable Hamiltonians, which we term displacement monotonicity condition, to study second order mean field games master equations. A rate of dissipation of a bilinear form is brought to bear a global (in time) well-posedness theory, based on a--priori uniform Lipschitz estimates on the solution in the measure variable. Displacement monotonicity being sometimes in dichotomy with the widely used Lasry-Lions monotonicity condition, the novelties of this work persist even when restricted to separable Hamiltonians.