In this paper we study the nonzero-sum Dynkin game in continuous time which is a two player non-cooperative game on stopping times. We show that it has a Nash equilibrium point for general stochastic processes. As an application, we consider the problem of pricing American game contingent claims...

We study the existence of optimal actions in a zero-sum game $\inf_\tau \sup_P E^P[X_\tau]$ between a stopper and a controller choosing a probability measure. In particular, we consider the optimal stopping problem $\inf_\tau \mathcal{E}(X_\tau)$ for a class of sublinear expectations...