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Stability analysis in a Bertrand duopoly with different product quality and heterogeneous expectations

  • Fanti, Luciano
  • Gori, Luca

We study the local stability properties of a duopoly game with price competition, different product quality and heterogeneous expectations. We show that the Nash equilibrium can loose stability through a flip bifurcation when the consumer’s type range increases. This result occurs irrespective of whether the high(low)-quality firm has either bounded rational (naïve) or naïve (bounded rational) expectations about the price that should be set in the future by the rival to maximise profits. Therefore, although, on the one hand, an increase in the consumer’s types range increases profits, on the other hand, it contributes to reduce the parametric stability region of the unique interior equilibrium. Moreover, we show that the stability region is larger when the high-quality firm has naïve expectations and the low-quality firm has bounded rational expectations. This implies that when the expectations formation mechanism of the high-quality firm becomes more complicated than the naïve one, and, in particular, it follows the mechanism proposed by Dixit (1986), the stability of the Nash equilibrium in a duopoly market with price competition becomes under increasing strain.

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Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 33480.

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Date of creation: 17 Sep 2011
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Handle: RePEc:pra:mprapa:33480
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  8. Agiza, H.N. & Elsadany, A.A., 2003. "Nonlinear dynamics in the Cournot duopoly game with heterogeneous players," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 320(C), pages 512-524.
  9. G.‐I. Bischi & M. Gallegati & A. Naimzada, 1999. "Symmetry‐breaking bifurcations and representativefirm in dynamic duopoly games," Annals of Operations Research, Springer, vol. 89(0), pages 252-271, January.
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  16. Motta, Massimo, 1993. "Endogenous Quality Choice: Price vs. Quantity Competition," Journal of Industrial Economics, Wiley Blackwell, vol. 41(2), pages 113-31, June.
  17. Fanti, Luciano & Gori, Luca, 2011. "The dynamics of a differentiated duopoly with quantity competition," MPRA Paper 33477, University Library of Munich, Germany.
  18. Dixit, Avinash K., 1978. "A Model of Duopoly Suggesting a Theory of Entry Barriers," The Warwick Economics Research Paper Series (TWERPS) 125, University of Warwick, Department of Economics.
  19. Luciano Fanti & Luca Gori, 2011. "The dynamics of a Bertrand duopoly with differentiated products and bounded rational firms revisited," Discussion Papers 2011/120, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
  20. Agliari, Anna & Chiarella, Carl & Gardini, Laura, 2006. "A re-evaluation of adaptive expectations in light of global nonlinear dynamic analysis," Journal of Economic Behavior & Organization, Elsevier, vol. 60(4), pages 526-552, August.
  21. Herguera, Inigo & Kujal, Praveen & Petrakis, Emmanuel, 2002. "Tariffs, quality reversals and exit in vertically differentiated industries," Journal of International Economics, Elsevier, vol. 58(2), pages 467-492, December.
  22. Zhang, Jixiang & Da, Qingli & Wang, Yanhua, 2007. "Analysis of nonlinear duopoly game with heterogeneous players," Economic Modelling, Elsevier, vol. 24(1), pages 138-148, January.
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