# Existence of Strong Randomized Equilibria in Mean-Field Games of Optimal Stopping with Common Noise

arXiv: https://arxiv.org/abs/2507.19123 · HTML: https://mlsanity.com/paper/2507.19123/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 25 Jul 2025.

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

- [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 study a mean-field game of optimal stopping and investigate the existence of strong solutions via a connection with the Bank-El Karoui's representation problem. Under certain continuity assumptions, where the common noise is generated by a countable partition, we show that a strong randomized mean-field equilibrium exists, in which the mean-field interaction term is adapted to the common noise and the stopping time is randomized. Furthermore, under suitable monotonicity assumptions and for a general common noise, we provide a comparative statics analysis of the set of strong mean-field equilibria with strict equilibrium stopping times.