IDEAS home Printed from https://ideas.repec.org/a/eee/apmaco/v436y2023ics0096300322005860.html
   My bibliography  Save this article

Pareto-based Stackelberg differential game for stochastic systems with multi-followers

Author

Listed:
  • Wang, Yu
  • Yan, Zhiguo

Abstract

This paper is concerned about a Pareto-based Stackelberg stochastic differential game with multi-followers, in which followers are cooperative relations. First of all, necessary and sufficient conditions for the existence of Pareto-based Stackelberg equilibrium are given for the general Pareto-based Stackelberg stochastic differential game problem. Next, we study the above game problem in the linear-quadratic (LQ) case and obtain a feedback form of Pareto-based Stackelberg equilibrium. The solvability of Riccati equations is guaranteed under some assumptions. Finally, the theoretical results are used to solve a national debt management problem.

Suggested Citation

  • Wang, Yu & Yan, Zhiguo, 2023. "Pareto-based Stackelberg differential game for stochastic systems with multi-followers," Applied Mathematics and Computation, Elsevier, vol. 436(C).
    • Handle: RePEc:eee:apmaco:v:436:y:2023:i:c:s0096300322005860
    DOI: 10.1016/j.amc.2022.127512
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0096300322005860
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.amc.2022.127512?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 search for a different version of it.

    References listed on IDEAS

    as
    1. Chen, Lv & Shen, Yang, 2019. "Stochastic Stackelberg differential reinsurance games under time-inconsistent mean–variance framework," Insurance: Mathematics and Economics, Elsevier, vol. 88(C), pages 120-137.
    2. Wang, Guangchen & Wang, Wencan & Yan, Zhiguo, 2021. "Linear quadratic control of backward stochastic differential equation with partial information," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    3. Øksendal, Bernt & Sandal, Leif & Ubøe, Jan, 2013. "Stochastic Stackelberg equilibria with applications to time-dependent newsvendor models," Journal of Economic Dynamics and Control, Elsevier, vol. 37(7), pages 1284-1299.
    4. Zhang, Huanjun & Yan, Zhiguo, 2020. "Backward stochastic optimal control with mixed deterministic controller and random controller and its applications in linear-quadratic control," Applied Mathematics and Computation, Elsevier, vol. 369(C).
    5. Kai Du & Zhen Wu, 2019. "Linear-Quadratic Stackelberg Game for Mean-Field Backward Stochastic Differential System and Application," Mathematical Problems in Engineering, Hindawi, vol. 2019, pages 1-17, February.
    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. Yueyang Zheng & Jingtao Shi, 2020. "A Stackelberg Game of Backward Stochastic Differential Equations with Applications," Dynamic Games and Applications, Springer, vol. 10(4), pages 968-992, December.
    2. Chen, Lv & Shen, Yang & Su, Jianxi, 2020. "A continuous-time theory of reinsurance chains," Insurance: Mathematics and Economics, Elsevier, vol. 95(C), pages 129-146.
    3. Liyuan Lin & Fangda Liu & Jingzhen Liu abd Luyang Yu, 2023. "The optimal reinsurance strategy with price-competition between two reinsurers," Papers 2305.00509, arXiv.org.
    4. Li Chen & Peipei Zhou & Hua Xiao, 2023. "Backward Stackelberg Games with Delay and Related Forward–Backward Stochastic Differential Equations," Mathematics, MDPI, vol. 11(13), pages 1-18, June.
    5. Huang, Pengyan & Wang, Guangchen & Wang, Wencan & Wang, Yu, 2023. "A linear-quadratic mean-field game of backward stochastic differential equation with partial information and common noise," Applied Mathematics and Computation, Elsevier, vol. 446(C).
    6. Wang, Ning & Zhang, Nan & Jin, Zhuo & Qian, Linyi, 2021. "Stochastic differential investment and reinsurance games with nonlinear risk processes and VaR constraints," Insurance: Mathematics and Economics, Elsevier, vol. 96(C), pages 168-184.
    7. Guan, Guohui & Hu, Xiang, 2022. "Equilibrium mean–variance reinsurance and investment strategies for a general insurance company under smooth ambiguity," The North American Journal of Economics and Finance, Elsevier, vol. 63(C).
    8. Bai, Yanfei & Zhou, Zhongbao & Xiao, Helu & Gao, Rui & Zhong, Feimin, 2022. "A hybrid stochastic differential reinsurance and investment game with bounded memory," European Journal of Operational Research, Elsevier, vol. 296(2), pages 717-737.
    9. Zongxia Liang & Xiaodong Luo, 2024. "Stackelberg reinsurance and premium decisions with MV criterion and irreversibility," Papers 2402.11580, arXiv.org.
    10. Zongxia Liang & Yi Xia & Bin Zou, 2024. "A Two-layer Stochastic Game Approach to Reinsurance Contracting and Competition," Papers 2405.06235, arXiv.org, revised Sep 2024.
    11. Kogan, Konstantin & Chernonog, Tatyana, 2019. "Competition under industry-stock-driven prevailing market price: Environmental consequences and the effect of uncertainty," European Journal of Operational Research, Elsevier, vol. 276(3), pages 929-946.
    12. Lu Yang & Chengke Zhang & Huainian Zhu, 2022. "Robust Stochastic Stackelberg Differential Reinsurance and Investment Games for an Insurer and a Reinsurer with Delay," Methodology and Computing in Applied Probability, Springer, vol. 24(1), pages 361-384, March.
    13. Wang, Guangchen & Wang, Wencan & Yan, Zhiguo, 2021. "Linear quadratic control of backward stochastic differential equation with partial information," Applied Mathematics and Computation, Elsevier, vol. 403(C).
    14. Guohui Guan & Zongxia Liang & Yilun Song, 2022. "A Stackelberg reinsurance-investment game under $\alpha$-maxmin mean-variance criterion and stochastic volatility," Papers 2212.14327, arXiv.org.
    15. Reza Azad Gholami & Leif Kristoffer Sandal & Jan Ubøe, 2022. "Construction of Equilibria in Strategic Stackelberg Games in Multi-Period Supply Chain Contracts," Games, MDPI, vol. 13(6), pages 1-26, October.
    16. Li, Danping & Young, Virginia R., 2022. "Stackelberg differential game for reinsurance: Mean-variance framework and random horizon," Insurance: Mathematics and Economics, Elsevier, vol. 102(C), pages 42-55.
    17. Sandal, Leif K. & Ubøe, Jan, 2012. "Stackelberg equilibria in a multiperiod vertical contracting model with uncertain and price-dependent demand," Discussion Papers 2012/2, Norwegian School of Economics, Department of Business and Management Science.
    18. Zhang, Caibin & Liang, Zhibin & Yuan, Yu, 2024. "Stochastic differential investment and reinsurance game between an insurer and a reinsurer under thinning dependence structure," European Journal of Operational Research, Elsevier, vol. 315(1), pages 213-227.
    19. Yuan, Yu & Han, Xia & Liang, Zhibin & Yuen, Kam Chuen, 2023. "Optimal reinsurance-investment strategy with thinning dependence and delay factors under mean-variance framework," European Journal of Operational Research, Elsevier, vol. 311(2), pages 581-595.
    20. Li, Danping & Young, Virginia R., 2021. "Bowley solution of a mean–variance game in insurance," Insurance: Mathematics and Economics, Elsevier, vol. 98(C), pages 35-43.

    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:apmaco:v:436:y:2023:i:c:s0096300322005860. 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: https://www.journals.elsevier.com/applied-mathematics-and-computation .

    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.