A Nonzero-Sum Extension of Dynkin's Stopping Problem

We consider two-person nonzero-sum stopping games for random sequences. The problem is divided into two cases with regard to underlying sequences. In the first case with infinite horizon and in the second one with finite stages we find equilibrium points and show that the corresponding equilibrium values satisfy certain value-relations. The values are constructed by the backward inductions. Also in both cases with infinite horizon we give sufficient conditions for a pair of stopping times to be an equilibrium point in terms of value-relation. Finally independent and Markov models are dealt with and especially in the latter the existence theorem for equilibrium points of the second case is given under suitable conditions.