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

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  • Luciano Fanti
  • Luca Gori

Abstract

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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Bibliographic Info

Paper provided by Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy in its series Discussion Papers with number 2011/122.

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Date of creation: 09 Jan 2011
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Handle: RePEc:pie:dsedps:2011/122

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Keywords: Bifurcation; Different product quality; Duopoly; Heterogeneous players; Price competition.;

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  1. Wauthy, Xavier, 1996. "Quality Choice in Models of Vertical Differentiation," Journal of Industrial Economics, Wiley Blackwell, vol. 44(3), pages 345-53, September.
  2. 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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  13. Fanti, Luciano & Gori, Luca, 2011. "The dynamics of a Bertrand duopoly with differentiated products and bounded rational firms revisited," MPRA Paper 33268, University Library of Munich, Germany.
  14. Herguera, Inigo & Kujal, Praveen & Petrakis, Emmanuel, 2000. "Quantity restrictions and endogenous quality choice," International Journal of Industrial Organization, Elsevier, vol. 18(8), pages 1259-1277, December.
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