Before revision:  Under slightly stronger assumptions, the optimal switching formulation is used to prove the existence of a saddle point and a connection is made to the classical "Mokobodski's hypothesis". Results are illustrated by comparison to numerical solutions of three specific Dynkin games which have appeared in recent papers, including an example of a game option with payoff dependent on a jump-diffusion process .
After revision:  Under slightly stronger assumptions, the optimal switching formulation is used to prove the existence of a saddle point in an optimal stopping (Dynkin) game. Sufficient conditions for the game's value to be continuous with respect to the time horizon are obtained using recent results on norm estimates for doubly reflected backward stochastic differential equations. This theory is then demonstrated numerically for the special cases of cancellable call and put options in a Black-Scholes market .