IDEAS home Printed from https://ideas.repec.org/a/wsi/igtrxx/v12y2010i04ns0219198910002726.html
   My bibliography  Save this article

Nonlinear Duopoly Games With Advertisement Revisited

Author

Listed:
  • AKIO MATSUMOTO

    (Department of Economics, Chuo University, 742-1, Higashi-Nakano, Hachioji, Tokyo, 192-0393, Japan)

  • FERENC SZIDAROVSZKY

    (Department of Systems and Industrial Engineering, University of Arizona, Tucson, AZ, 85721-0020, USA)

Abstract

This study reconsiders a duopoly model with advertisement introduced earlier by Ahmed, Agiza and Hassan [1999]. It demonstrates three major findings. The first is that the model can be destabilized via either flip bifurcation or Hopf bifurcation. The second is that a half-pitchfork bifurcation of the output occurs when the advertisement dynamics is periodic and the nonlinearity of the output dynamics becomes stronger. Finally the third is that the existence of attractor and the coexistence of attracting sets are the main features of the model when it is locally unstable.

Suggested Citation

  • Akio Matsumoto & Ferenc Szidarovszky, 2010. "Nonlinear Duopoly Games With Advertisement Revisited," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 12(04), pages 363-384.
    • Handle: RePEc:wsi:igtrxx:v:12:y:2010:i:04:n:s0219198910002726
    DOI: 10.1142/S0219198910002726
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0219198910002726
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0219198910002726?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.

    More about this item

    Keywords

    Nonlinear duopoly game; advertisement dynamics; Hopf bifurcation; multistability;
    All these keywords.

    JEL classification:

    • B4 - Schools of Economic Thought and Methodology - - Economic Methodology
    • C0 - Mathematical and Quantitative Methods - - General
    • C6 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D5 - Microeconomics - - General Equilibrium and Disequilibrium
    • D7 - Microeconomics - - Analysis of Collective Decision-Making
    • M2 - Business Administration and Business Economics; Marketing; Accounting; Personnel Economics - - Business Economics

    Statistics

    Access and download statistics

    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:wsi:igtrxx:v:12:y:2010:i:04:n:s0219198910002726. 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.

    We have no bibliographic references for this item. You can help adding them by using 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: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/igtr/igtr.shtml .

    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.