NONLINEAR DUOPOLY GAMES WITH ADVERTISEMENT REVISITED

Akio Matsumoto () and Ferenc Szidarovszky ()
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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

International Game Theory Review (IGTR), 2010, vol. 12, issue 04, 363-384

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.

Keywords: Nonlinear duopoly game; advertisement dynamics; Hopf bifurcation; multistability (search for similar items in EconPapers)
JEL-codes: B4 C0 C6 C7 D5 D7 M2 (search for similar items in EconPapers)
Date: 2010
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DOI: 10.1142/S0219198910002726

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