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Nonlinear Duopoly Games With Advertisement Revisited

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  • 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)

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    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.

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    Bibliographic Info

    Article provided by World Scientific Publishing Co. Pte. Ltd. in its journal International Game Theory Review.

    Volume (Year): 12 (2010)
    Issue (Month): 04 ()
    Pages: 363-384

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    Handle: RePEc:wsi:igtrxx:v:12:y:2010:i:04:p:363-384

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    Related research

    Keywords: Nonlinear duopoly game; advertisement dynamics; Hopf bifurcation; multistability;

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