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

TL;DR

This paper proves the existence of strong randomized equilibria in mean-field games of optimal stopping with common noise, using a connection to the Bank-El Karoui representation problem and analyzing equilibrium properties.

Contribution

It establishes the existence of strong solutions under certain conditions and provides a comparative statics analysis for general common noise.

Findings

Strong randomized mean-field equilibria exist under specified assumptions.

Equilibrium interactions are adapted to common noise and involve randomized stopping times.

Comparative statics reveal how equilibrium sets change with parameters.

Abstract

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.