Zero-sum stopping game associated with threshold probability

We consider a zero-sum stopping game (Dynkin’s game) with a threshold probability criterion in discrete time stochastic processes. We first obtain fundamental characterization of value function of the game and optimal stopping times for both players as the result of the classical Dynkin’s game, but the value function of the game and the optimal stopping time for each player depend upon a threshold value. We also give properties of the value function of the game with respect to threshold value. These are applied to an independent model and we explicitly find a value function of the game and optimal stopping times for both players in a special example.