Stopping
Games in Continuous Time

Rida
Laraki and Eilon Solan

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.