Two-person zero-sum risk-sensitive stochastic games with incomplete reward information on one side

Abstract

This study considers zero-sum risk-sensitive discrete-time stochastic games with incomplete reward information on one side. We show the existence of the value function, derive a new Shapley equation, and prove that the value function solves the Shapley equation, which is used to construct an optimal policy for the informed player. For the uninformed player, we construct an optimal policy by introducing a dual game. Finally, we give an example to illustrate the effects of the reward information and risk-sensitive parameters on the value function and optimal policies.