# Mean field games via controlled martingale problems: Existence of Markovian equilibria

arXiv: https://arxiv.org/abs/1404.2642 · HTML: https://mlsanity.com/paper/1404.2642/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 9 Apr 2014.

## Built on by (most cited first, 2 of 2)

- [Learning Correlated Equilibria in Mean-Field Games](https://mlsanity.com/paper/2208.10138/) (2022)
- [Graphon Mean Field Games with a Representative Player: Analysis and Learning Algorithm](https://mlsanity.com/paper/2405.08005/) (2024)

## Abstract (arXiv)

Mean field games are studied in the framework of controlled martingale problems, and general existence theorems are proven in which the equilibrium control is Markovian. The framework is flexible enough to include degenerate volatility, which may depend on both the control and the mean field. The objectives need not be strictly convex, and the mean field interactions considered are nonlocal and Wasserstein-continuous. When the volatility is nondegenerate, continuity assumptions may be weakened considerably. The proofs first use relaxed controls to establish existence. Then, using a convexity assumption and measurable selection arguments, strict (non-relaxed) Markovian equilibria are constructed from relaxed equilibria.