Numerical Calculation of Optimal Policy Pairs in Zero-sum Stochastic Games with Varying Discount Factors

Abstract

In this study, the numerical calculation of optimal policy pairs in two-person zero-sum stochastic games with unbounded reward functions and state-dependent discount factors are studied. First, the expected discount criterion, $\epsilon$ −optimal values, and policy pairs are defined for zero-sum stochastic game model. Then, an iterative algorithm is given and the correctness of the algorithm is verified. At last, an example of inventory system is stated, the numerical simulation is obtained according to the iterative algorithm steps, and the difference between varying discount factors and a constant discount factor is obtained in further discussion.