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

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 problem, first introduced by Irle [6] for discrete-time Markov processes and later revisited by Miclo & Villeneuve [8] for continuous-time Markov processes on general state spaces. This paper focuses on a game driven by a homogeneous Markov process taking values in a finite state space and also discusses about the number of iterations needed. Illustrated computational implementations for a few particular examples are also provided.

💡 Research Summary

The paper addresses the computational problem of determining the value function and optimal stopping regions in a zero‑sum stopping game played on a finite‑state continuous‑time homogeneous Markov chain. Two players, a sup‑player and an inf‑player, choose stopping times τ and γ respectively to maximize or minimize the discounted payoff
Rₓ(τ,γ)=Eₓ