Two Player Non Zero-sum Stopping Games in Discrete Time, Annals of Probability
We prove that every two-player nonzero sum stopping game in discrete time admits an ?-equilibrium in randomized strategies for every ?>0. We use a stochastic variation of Ramsey's theorem, which enables us to reduce the problem to that of studying properties of ?-equilibria in a simple class of stochastic games with finite state space.
Eran Shmaya, Eilon Solan
Shmaya, Eran, and Eilon Solan. 2004. Two Player Non Zero-sum Stopping Games in Discrete Time. Annals of Probability. 32(3B): 2733-2764.