Zero-Sum Average Semi-Markov Games: Fixed-Point Solutions of the Shapley Equation

Abstract

This paper deals with zero-sum average semi-Markov games with Borel state and action spaces, unbounded payoffs, and mean holding times. A solution to the Shapley equation is obtained via the Banach fixed-point theorem assuming that the model satisfies a Lyapunov-like condition, a growth hypothesis on the payoff function, and the mean holding times, besides standard continuity and compactness requirements.