We prove that every two-player nonzero–sum stopping game in discrete time admits an ɛ-equilibrium in randomized strategies for every ɛ>0. We use a stochastic variation of Ramsey’s theorem, which enables us to reduce the problem to that of studying properties of ɛ-equilibria in a simple class of stochastic games with finite state space.
"Two-player nonZero–sum stopping games in discrete time." Ann. Probab. 32 (3B) 2733 - 2764, July 2004. https://doi.org/10.1214/009117904000000162