# Convergence to the Mean Field Game Limit: A Case Study

arXiv: https://arxiv.org/abs/1806.00817 · HTML: https://mlsanity.com/paper/1806.00817/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Jun 2018.

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

- [Learning in Herding Mean Field Games: Single-Loop Algorithm with Finite-Time Convergence Analysis](https://mlsanity.com/paper/2408.04780/) (2024)
- [Prediction-Enhanced Monte Carlo: A Machine Learning View on Control Variate](https://mlsanity.com/paper/2412.11257/) (2024)

## Abstract (arXiv)

We study the convergence of Nash equilibria in a game of optimal stopping. If the associated mean field game has a unique equilibrium, any sequence of n-player equilibria converges to it as n→∞. However, both the finite and infinite player versions of the game often admit multiple equilibria. We show that mean field equilibria satisfying a transversality condition are limit points of n-player equilibria, but we also exhibit a remarkable class of mean field equilibria that are not limits, thus questioning their interpretation as "large n" equilibria.