A forward algorithm for a class of Markov zero-sum stopping games

Abstract 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.