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

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  • 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
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    References listed on IDEAS

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    1. 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).
    2. 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.
    3. 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).
    4. 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.
    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.
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