Zero-sum infinite-horizon discounted piecewise deterministic Markov games

Yonghui Huang (), Zhaotong Lian () and Xianping Guo ()
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Yonghui Huang: Sun Yat-Sen University
Zhaotong Lian: University of Macau
Xianping Guo: Sun Yat-Sen University

Mathematical Methods of Operations Research, 2023, vol. 97, issue 2, No 3, 179-205

Abstract: Abstract This paper is devoted to zero-sum piecewise deterministic Markov games with Borel state and action spaces, where the expected infinite-horizon discounted payoff criterion is considered. Both the transition rate and payoff rate are allowed to be unbounded. The policies of the two players are history-dependent, and the controls continuously act on the transition rate and the payoff rate. Under suitable conditions, Dynkin’s formula and the comparison theorem are developed in our setup, via which the game is shown to have the value function as the unique solution to the associated Shapley equation. By the Shapley equation in the form of a differential equation, we establish the existence of a saddle point with a very simple form, which only depends on the current state and can be applied at any time. A potential algorithm for computing saddle points is proposed.

Keywords: Piecewise deterministic Markov games; Zero sum; Unbounded transition rate; Shapley equation; Saddle point; 91A15; 91A25 (search for similar items in EconPapers)
Date: 2023
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DOI: 10.1007/s00186-023-00809-0

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