IDEAS home Printed from https://ideas.repec.org/a/eee/matcom/v245y2026icp464-482.html

N-player Pareto game for the discrete-time Markov jump systems with multiplicative noises using off-policy reinforcement learning

Author

Listed:
  • Bo, Chunling
  • Lin, Yaning
  • Li, Yuxia

Abstract

This paper investigates a discrete-time N-player Pareto cooperative game problem for the Markov jump systems with multiplicative noises. First, utilizing the convexity condition, the Pareto cooperative game problem is transformed into a weighted sum optimal control problem. To address this problem, we reconstruct the system and prove that the optimal control gains do not change after the reconstruction. Compared with the traditional policy iteration algorithm which is sensitive to probing noise, the proposed model-based off-policy algorithm yields unbiased solution to Pareto cooperative game problem when probing noise is added. Due to the complexity of the jump systems and the multiplicative noises, relying on its dynamic information may cause policy bias in some situations. To further eliminate the dependence on the system information of model-based off-policy algorithm, a model-free off-policy algorithm is designed based on the properties of the trace using only information of the system states and inputs. In addition, the convergence of the proposed algorithm and the stability of the system under each iteration step are proved. Finally, practical numerical examples are given to show the effectiveness of the algorithm.

Suggested Citation

  • Bo, Chunling & Lin, Yaning & Li, Yuxia, 2026. "N-player Pareto game for the discrete-time Markov jump systems with multiplicative noises using off-policy reinforcement learning," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 245(C), pages 464-482.
    • Handle: RePEc:eee:matcom:v:245:y:2026:i:c:p:464-482
    DOI: 10.1016/j.matcom.2026.02.020
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0378475426000662
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.matcom.2026.02.020?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to

    for a different version of it.

    References listed on IDEAS

    as
    1. Wang, Jie & Chen, Xin, 2023. "H∞ consensus for stochastic Markov jump multi-agent systems with imperfect time-varying transition probabilities and multiplicative noise," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    2. Hu, Po & Ma, Hongbin & Yang, Xiaoguang & Mu, Yifen, 2024. "Pareto efficiency of infinite-horizon cooperative stochastic differential games with Markov jumps and Poisson jumps," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 225(C), pages 480-494.
    3. Fabio Barbieri & Oswaldo L. V. Costa, 2018. "Optimal control with constrained total variance for Markov jump linear systems with multiplicative noises," International Journal of Systems Science, Taylor & Francis Journals, vol. 49(6), pages 1178-1187, April.
    4. Wang, Yu & Yan, Zhiguo, 2023. "Pareto-based Stackelberg differential game for stochastic systems with multi-followers," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Pengyan Huang & Guangchen Wang & Shujun Wang, 2025. "Pareto Game of Stochastic Differential System with Terminal State Constraint," Journal of Optimization Theory and Applications, Springer, vol. 205(1), pages 1-30, April.
    2. Zhongmiao Sun & Qi Xu & Jinrong Liu, 2023. "Dynamic supervision of counterfeit products based on blockchain technology: A differential game on goodwill accumulation," PLOS ONE, Public Library of Science, vol. 18(10), pages 1-53, October.

    More about this item

    Keywords

    ;
    ;
    ;
    ;

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:eee:matcom:v:245:y:2026:i:c:p:464-482. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Catherine Liu (email available below). General contact details of provider: http://www.journals.elsevier.com/mathematics-and-computers-in-simulation/ .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.