Communicating Zero-Sum Product Stochastic Games

TL;DR

This paper investigates zero-sum stochastic games with communication properties, establishing the existence of uniform values in strongly communicating games and showing potential failure in weakly communicating ones.

Contribution

It introduces new results on the existence of uniform and asymptotic values based on communication properties of the game.

Findings

Uniform value exists in strongly communicating games.

Asymptotic and uniform values may not exist in weakly communicating games.

Communication structure critically affects value existence.

Abstract

We study two classes of zero-sum stochastic games with compact action sets and a finite product state space. These two classes assume a communication property on the state spaces of the players. For strongly communicating on one side games, we prove the existence of the uniform value. For weakly communicating on both sides games, we prove that the asymptotic value, and therefore the uniform value, may fail to exist.