In this paper we propose a new efficient algorithm to compute the value function for zero-sum stopping games featuring two players with opposing interests. This can be seen as a game version of the ‘forward algorithm’ for (one-player) optimal stopping problems, first introduced by Irle (2006) for discrete-time Markov chains and later revisited by Miclo and Villeneuve (2021) for continuous-time Markov processes on general state spaces. This paper focuses on a game driven by a homogeneous continuous-time Markov chain taking values in a finite state space and also discusses the number of iterations needed. Illustrated computational implementations for a few particular examples are also provided.

In this paper we study continuous-time two-player zero-sum optimal switching games on a finite horizon. Using the theory of doubly reflected backward stochastic differential equations with interconnected barriers, we show that this game has a value and an equilibrium in the players’ switching controls.

This paper uses recent results on continuous-time finite-horizon optimal switching problems with negative switching costs 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.