A Mean Field Game of Optimal Stopping

TL;DR

This paper develops a mean field game model for optimal stopping where agents' decisions depend on the proportion of others who have stopped, providing insights into equilibrium uniqueness and population dynamics.

Contribution

It introduces a new mean field game framework for optimal stopping with a structural monotonicity assumption, simplifying equilibrium analysis.

Findings

Equilibria can be characterized by a simple equation involving the distribution of idiosyncratic noise.

Under certain conditions, the model ensures the uniqueness of equilibria.

Examples demonstrate the dynamics and stability of equilibria in the population.

Abstract

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.