IDEAS home Printed from https://ideas.repec.org/a/eee/chsofr/v171y2023ics0960077923003910.html
   My bibliography  Save this article

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

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0960077923003910
    Download Restriction: Full text for ScienceDirect subscribers only
    File URL: https://libkey.io/10.1016/j.chaos.2023.113490?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. 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, 2021. "Optimal control for uncertain random singular systems with multiple time-delays," Chaos, Solitons & Fractals, Elsevier, vol. 152(C).
    3. 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).
    4. 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).
    5. 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, September.
    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. Masahiko Hattori & Yasuhito Tanaka, 2019. "General analysis of dynamic oligopoly with sticky price," Economics Bulletin, AccessEcon, vol. 39(4), pages 2990-2998.
    2. Régis Chenavaz & Corina Paraschiv & Gabriel Turinici, 2017. "Dynamic Pricing of New Products in Competitive Markets: A Mean-Field Game Approach," Working Papers hal-01592958, HAL.
    3. Reinhard Neck & Dmitri Blueschke, 2014. "“Haircuts” for the EMU periphery: virtue or vice?," Empirica, Springer;Austrian Institute for Economic Research;Austrian Economic Association, vol. 41(2), pages 153-175, May.
    4. A. J. Novak & G. Feichtinger & G. Leitmann, 2010. "A Differential Game Related to Terrorism: Nash and Stackelberg Strategies," Journal of Optimization Theory and Applications, Springer, vol. 144(3), pages 533-555, March.
    5. Gerhard Sorger, 2005. "A dynamic common property resource problem with amenity value and extraction costs," International Journal of Economic Theory, The International Society for Economic Theory, vol. 1(1), pages 3-19, March.
    6. Denis Claude & Charles Figuières & Mabel Tidball, 2008. "Short-run stick and long-run carrot policy: the role of initial conditions," Working Papers 08-04, LAMETA, Universtiy of Montpellier, revised Feb 2008.
    7. Stergios Athanassoglou & Glenn Sheriff & Tobias Siegfried & Woonghee Huh, 2012. "Optimal Mechanisms for Heterogeneous Multi-Cell Aquifers," Environmental & Resource Economics, Springer;European Association of Environmental and Resource Economists, vol. 52(2), pages 265-291, June.
    8. S. Luckraz, 2008. "Process Spillovers and Growth," Journal of Optimization Theory and Applications, Springer, vol. 139(2), pages 315-335, November.
    9. Mukherjee, Arka & Chauhan, Satyaveer S., 2021. "The impact of product recall on advertising decisions and firm profit while envisioning crisis or being hazard myopic," European Journal of Operational Research, Elsevier, vol. 288(3), pages 953-970.
    10. Laussel, Didier & Resende, Joana, 2014. "Dynamic price competition in aftermarkets with network effects," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 106-118.
    11. Hassan Benchekroun & Farnaz Taherkhani, 2014. "Adaptation and the Allocation of Pollution Reduction Costs," Dynamic Games and Applications, Springer, vol. 4(1), pages 32-57, March.
    12. Francesco Caruso & Maria Carmela Ceparano & Jacqueline Morgan, 2017. "Uniqueness of Nash Equilibrium in Continuous Weighted Potential Games," CSEF Working Papers 471, Centre for Studies in Economics and Finance (CSEF), University of Naples, Italy, revised 18 Jun 2017.
    13. Niko Jaakkola & Florian Wagener, 2020. "All symmetric equilibria in differential games with public goods," Tinbergen Institute Discussion Papers 20-020/II, Tinbergen Institute.
    14. Javier Frutos & Guiomar Martín-Herrán, 2018. "Selection of a Markov Perfect Nash Equilibrium in a Class of Differential Games," Dynamic Games and Applications, Springer, vol. 8(3), pages 620-636, September.
    15. João Faria & Rajeev Goel, 2010. "Returns to networking in academia," Netnomics, Springer, vol. 11(2), pages 103-117, July.
    16. Johnson Kakeu & Gérard Gaudet, 2011. "The Quest for Hegemony Among Countries and Global Pollution," Dynamic Games and Applications, Springer, vol. 1(4), pages 498-513, December.
    17. Nair, Anand & Narasimhan, Ram, 2006. "Dynamics of competing with quality- and advertising-based goodwill," European Journal of Operational Research, Elsevier, vol. 175(1), pages 462-474, November.
    18. R. Cellini & L. Lambertini & G. Leitmann, 2004. "Perfect Uncontrollable Differential Games," Working Papers 509, Dipartimento Scienze Economiche, Universita' di Bologna.
    19. Pineau, Pierre-Olivier & Rasata, Hasina & Zaccour, Georges, 2011. "Impact of some parameters on investments in oligopolistic electricity markets," European Journal of Operational Research, Elsevier, vol. 213(1), pages 180-195, August.
    20. Julio Huato, 2023. "Inequality and Growth: A Two-Player Dynamic Game with Production and Appropriation," Papers 2304.01855, arXiv.org.

    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:chsofr:v:171:y:2023:i:c:s0960077923003910. 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: Thayer, Thomas R. (email available below). General contact details of provider: https://www.journals.elsevier.com/chaos-solitons-and-fractals .

    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.