Zero-Sum Games for piecewise deterministic Markov decision processes with risk-sensitive finite-horizon cost criterion

TL;DR

This paper studies two-player zero-sum stochastic games for piecewise deterministic Markov decision processes with a risk-sensitive finite-horizon cost, establishing the existence of a value and optimal strategies under broad conditions.

Contribution

It proves the existence of the game value and saddle-point equilibrium for risk-sensitive PDMs with unbounded transition and cost rates, extending previous results.

Findings

Existence of the game value and saddle-point equilibrium.

Validation of extended Feynman-Kac formula for unbounded functions.

Results hold under mild conditions for general state spaces.

Abstract

This paper investigates the two-person zero-sum stochastic games for piece-wise deterministic Markov decision processes with risk-sensitive finite-horizon cost criterion on a general state space. Here, the transition and cost/reward rates are allowed to be un-unbounded from below and above. Under some mild conditions, we show the existence of the value of the game and an optimal randomized Markov saddle-point equilibrium in the class of all admissible feedback strategies. By studying the corresponding risk-sensitive finite-horizon optimal differential equations out of a class of possibly unbounded functions, to which the extended Feynman-Kac formula is also justified to hold, we obtain our required results.