# Mean Field Games with a Dominating Player

arXiv: https://arxiv.org/abs/1404.4148 · HTML: https://mlsanity.com/paper/1404.4148/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 16 Apr 2014.

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

- [Learning Discrete-Time Major-Minor Mean Field Games](https://mlsanity.com/paper/2312.10787/) (2023)

## Abstract (arXiv)

In this article, we consider mean field games between a dominating player and a group of representative agents, each of which acts similarly and also interacts with each other through a mean field term being substantially influenced by the dominating player. We first provide the general theory and discuss the necessary condition for the optimal controls and game condition by adopting adjoint equation approach. We then present a special case in the context of linear-quadratic framework, in which a necessary and sufficient condition can be asserted by stochastic maximum principle; we finally establish the sufficient condition that guarantees the unique existence of the equilibrium control. The proof of the convergence result of finite player game to mean field counterpart is provided in Appendix.