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Uncertain stochastic hybrid differential game system with V-n jumps: Saddle point equilibrium strategies and application to advertising duopoly game

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  • Jia, Zhifu
  • Liu, Xinsheng

Abstract

This paper focuses on the saddle point equilibrium strategies for uncertain stochastic hybrid differential game systems under chance theory. We consider systems with dynamics described by both an uncertain differential equation with V-n jumps (UDEV) and a stochastic differential equation (SDE), with linear and quadratic performance index functions. Based on chance theory and the equation of optimality of uncertain stochastic hybrid optimal control model, the saddle equilibrium equation for general uncertain stochastic hybrid differential game system is established. Furthermore, three classes of differential game models are discussed by using equilibrium equation. Finally, an advertising duopoly game problem as an application is provided, the corresponding optimal profit difference value and advertising strategies are analyzed.

Suggested Citation

  • Jia, Zhifu & Liu, Xinsheng, 2023. "Uncertain stochastic hybrid differential game system with V-n jumps: Saddle point equilibrium strategies and application to advertising duopoly game," Chaos, Solitons & Fractals, Elsevier, vol. 171(C).
    • Handle: RePEc:eee:chsofr:v:171:y:2023:i:c:s0960077923003910
    DOI: 10.1016/j.chaos.2023.113490
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    References listed on IDEAS

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    1. Clemhout, S & Leitmann, G & Wan, H Y, Jr, 1971. "A Differential Game Model of Duopoly," Econometrica, Econometric Society, vol. 39(6), pages 911-938, November.
    2. Chen, Xin & Zhu, Yuanguo & Sheng, Linxue, 2021. "Optimal control for uncertain stochastic dynamic systems with jump and application to an advertising model," Applied Mathematics and Computation, Elsevier, vol. 407(C).
    3. Tian, Baodan & Zhang, Yong & Li, Jiamei, 2020. "Stochastic perturbations for a duopoly Stackelberg model," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 545(C).
    4. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, October.
    5. Chen, Xin & Zhu, Yuanguo, 2021. "Optimal control for uncertain random singular systems with multiple time-delays," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
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