Two Player Non Zero-Sum Stopping Games in Discrete Time

Eran Shmaya and Eilon Solan

We prove that every two player non zero-sum stopping game in discrete time admits an $\epsilon$-equilibrium in randomized strategies, for every e > 0.

We use a stochastic variation of Ramsey Theorem, which enables us to reduce the problem to that of studying properties of e-equilibria in a simple class of stochastic games with finite state space.