Multi-player stopping games in continuous time

TL;DR

This paper studies multi-player stopping games in continuous time where players observe others' actions before deciding when to stop, proving the existence of approximate Nash equilibria under certain conditions.

Contribution

It introduces a new class of continuous-time multi-player stopping games with observable strategies and establishes the existence of ε-Nash equilibria in pure strategies.

Findings

Existence of ε-Nash equilibria in pure strategies for the game.

Payoff functions are continuous in time, facilitating equilibrium analysis.

Players can adapt strategies based on observed behaviors.

Abstract

We consider multi-player stopping games in continuous time. Unlike Dynkin games, in our games the payoff of each player is revealed after all the players stop. Moreover, each player can adjust her own stopping strategy by observing other players' behaviors. Assuming the continuity of the payoff functions in time, we show that there always exists an $\eps$-Nash equilibrium in pure stopping strategies for any $\eps>0$.