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

Subrata Golui

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arXiv · 2405.08012

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

Subrata Golui

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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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Subrata Golui. 2024-05-10. Zero-Sum Games for piecewise deterministic Markov decision processes with risk-sensitive finite-horizon cost criterion. https://arxiv.org/abs/2405.08012

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