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

2024/05/10 by Subrata Golui, Golui, Subrata
Decision Sciences · #FOS: Mathematics #Optimization and Control (math.OC) #Probability (math.PR) #Simulation Techniques and Applications

paper · pdf · doi:10.48550/arxiv.2405.08012

openalex publication_date 2024/05/10 · openalex created_date 2024/05/16 · openalex updated_date 2026/07/28

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.

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