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Zero-sum infinite-horizon discounted piecewise deterministic Markov games

Author

Listed:
  • Yonghui Huang

    (Sun Yat-Sen University)

  • Zhaotong Lian

    (University of Macau)

  • Xianping Guo

    (Sun Yat-Sen University)

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.

Suggested Citation

  • Yonghui Huang & Zhaotong Lian & Xianping Guo, 2023. "Zero-sum infinite-horizon discounted piecewise deterministic Markov games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 97(2), pages 179-205, April.
    • Handle: RePEc:spr:mathme:v:97:y:2023:i:2:d:10.1007_s00186-023-00809-0
    DOI: 10.1007/s00186-023-00809-0
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    References listed on IDEAS

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    3. Alain Haurie & Jacek B Krawczyk & Georges Zaccour, 2012. "Games and Dynamic Games," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 8442, February.
    4. Fabien Gensbittel & Jérôme Renault, 2015. "The Value of Markov Chain Games with Incomplete Information on Both Sides," Mathematics of Operations Research, INFORMS, vol. 40(4), pages 820-841, October.
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