Zero-Sum Markov Games with Random State-Actions-Dependent Discount Factors: Existence of Optimal Strategies

Abstract

This work deals with a class of discrete-time zero-sum Markov games under a discounted optimality criterion with random state-actions-dependent discount factors of the form $$\tilde{\alpha }(x_{n},a_{n},b_{n},\xi _{n+1})$$ , where $$x_{n}, a_{n}, b_{n}$$ , and $$\xi _{n+1}$$ are the state, the actions of players, and a random disturbance at time n, respectively, taking values in Borel spaces. Assuming possibly unbounded payoff, we prove the existence of a value of the game as well as a stationary pair of optimal strategies.