# A Mean Field Game of Optimal Stopping

arXiv: https://arxiv.org/abs/1605.09112 · HTML: https://mlsanity.com/paper/1605.09112/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 30 May 2016.

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

- [Deep Learning for Mean Field Games and Mean Field Control with Applications to Finance](https://mlsanity.com/paper/2107.04568/) (2021)
- [Mean field games as a tool for AI safety: a worked example from the July 2026 Hugging Face incident](https://mlsanity.com/paper/2610.00902/) (2026)

## Abstract (arXiv)

We formulate a stochastic game of mean field type where the agents solve optimal stopping problems and interact through the proportion of players that have already stopped. Working with a continuum of agents, typical equilibria become functions of the common noise that all agents are exposed to, whereas idiosyncratic randomness can be eliminated by an Exact Law of Large Numbers. Under a structural monotonicity assumption, we can identify equilibria with solutions of a simple equation involving the distribution function of the idiosyncratic noise. Solvable examples allow us to gain insight into the uniqueness of equilibria and the dynamics in the population.