Stopping games in continuous time

TL;DR

This paper establishes the existence of the value in continuous-time two-player zero-sum stopping games with right-continuous payoffs, without imposing additional conditions, and demonstrates the existence of near-optimal randomized stopping strategies.

Contribution

It proves the existence of the game value under minimal assumptions and introduces simple epsilon-approximate randomized stopping times, extending previous results.

Findings

Value exists for right-continuous payoffs.

Players have simple epsilon-optimal randomized strategies.

No conditions on payoff relations are required.

Abstract

We study two-player zero-sum stopping games in continuous time and infinite horizon. We prove that the value in randomized stopping times exists as soon as the payoff processes are right-continuous. In particular, as opposed to existing literature, we do not assume any conditions on the relations between the payoff processes. We also show that both players have simple epsilon- optimal randomized stopping times; namely, randomized stopping times which are small perturbations of non-randomized stopping times.