IDEAS home Printed from https://ideas.repec.org/a/bpj/jossai/v3y2015i2p154-163n5.html
   My bibliography  Save this article

Composite Stackelberg Strategy for Singularly Perturbed Bilinear Quadratic Systems

Author

Listed:
  • Bin Ning

    (School of Management, Guangdong University of Technology, Guangzhou, 510520, China)

  • Zhang Chengke

    (School of Commerce & Economics, Guangdong University of Technology, Guangzhou, 510520, China)

  • Zhu Huainian

    (School of Management, Guangdong University of Technology, Guangzhou, 510520, China)

  • Mo Zan

    (School of Management, Guangdong University of Technology, Guangzhou, 510520, China)

Abstract

Based on singularly perturbed bilinear quadratic problems, this paper proposes to decompose the full-order system into two subsystems of a slow-time and fast-time scale. Utilizing the fixed point iterative algorithm to solve cross-coupled algebraic Riccati equations, equilibrium strategies of the two subsystems can be obtained, and further the composite strategy of the original full-order system. It was proved that such a composite strategy formed an o(ε) (near) Stackelberg equilibrium, and a numerical result of the algorithm was presented in the end.

Suggested Citation

  • Bin Ning & Zhang Chengke & Zhu Huainian & Mo Zan, 2015. "Composite Stackelberg Strategy for Singularly Perturbed Bilinear Quadratic Systems," Journal of Systems Science and Information, De Gruyter, vol. 3(2), pages 154-163, April.
    • Handle: RePEc:bpj:jossai:v:3:y:2015:i:2:p:154-163:n:5
    DOI: 10.1515/JSSI-2015-0154
    as

    Download full text from publisher

    File URL: https://doi.org/10.1515/JSSI-2015-0154
    Download Restriction: no
    File URL: https://libkey.io/10.1515/JSSI-2015-0154?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
    ---><---

    References listed on IDEAS

    as
    1. William M. McEneaney, 1997. "A Robust Control Framework for Option Pricing," Mathematics of Operations Research, INFORMS, vol. 22(1), pages 202-221, February.
    2. Chander, Parkash, 1983. "The nonlinear input-output model," Journal of Economic Theory, Elsevier, vol. 30(2), pages 219-229, August.
    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. Yaw M. Mensah, 1988. "Exercising budgetary control in automated production environments," Contemporary Accounting Research, John Wiley & Sons, vol. 5(1), pages 222-249, September.
    2. Zhang, Jin Shui, 2011. "The analytical solution of balanced growth of non-linear dynamic multi-sector economic model," Economic Modelling, Elsevier, vol. 28(1), pages 410-421.
    3. Kaj Nystrom & Mikko Parviainen, 2014. "Tug-of-war, market manipulation and option pricing," Papers 1410.1664, arXiv.org.
    4. Zhang, Jin Shui, 2011. "The analytical solution of balanced growth of non-linear dynamic multi-sector economic model," Economic Modelling, Elsevier, vol. 28(1-2), pages 410-421, January.
    5. Guerra, Ana-Isabel & Sancho, Ferran, 2014. "An operational, nonlinear input–output system," Economic Modelling, Elsevier, vol. 41(C), pages 99-108.
    6. Roorda, B. & Engwerda, J.C. & Schumacher, J.M., 1999. "Performance of Delta-hedging strategies in interval models - A robustness study," Discussion Paper 1999-05, Tilburg University, Center for Economic Research.
    7. Esteban Fernandez-Vazquez, 2015. "Empirical Estimation Of Non-Linear Input--Output Models: An Entropy Econometrics Approach," Economic Systems Research, Taylor & Francis Journals, vol. 27(4), pages 508-524, December.
    8. Zhang, Jin shui, 2001. "Iterative method for finding the balanced growth solution of the non-linear dynamic input-output model and the dynamic CGE model," Economic Modelling, Elsevier, vol. 18(1), pages 117-132, January.
    9. Li Da, Xu & Cheng, Chuwang & Tang, Bingyong, 2000. "A linear matrix inequality approach for robust control of systems with delayed states," European Journal of Operational Research, Elsevier, vol. 124(2), pages 332-341, July.

    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:bpj:jossai:v:3:y:2015:i:2:p:154-163:n:5. 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: Peter Golla (email available below). General contact details of provider: https://www.degruyter.com .

    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.