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

TL;DR

This paper introduces an efficient forward algorithm for computing the value function in zero-sum Markov stopping games, extending the concept from single-player optimal stopping to a two-player game setting.

Contribution

It develops a novel forward algorithm tailored for Markov zero-sum stopping games, including analysis of iteration complexity and practical computational examples.

Findings

Algorithm effectively computes game values in finite state spaces.

Provides bounds on the number of iterations needed.

Demonstrates applicability through specific examples.

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 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.