Two-person zero-sum stochastic games with varying discount factors

Abstract

<abstract><p>In this paper, two-person zero-sum Markov games with Borel state space and action space, unbounded reward function and state-dependent discount factors are studied. The optimal criterion is expected discount criterion. Firstly, sufficient conditions for the existence of optimal policies are given for the two-person zero-sum Markov games with varying discount factors. Then, the existence of optimal policies is proved by Banach fixed point theorem. Finally, we give an example for reservoir operations to illustrate the existence results.</p></abstract>