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

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  • Fanti, Luciano
  • Gori, Luca

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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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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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. Ornella Tarola & Jean Gabszewicz & Didier Laussel, 2011. "To Acquire, or To Compete? An Entry Dilemma," Journal of Industry, Competition and Trade, Springer, vol. 11(4), pages 369-383, December.
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  7. Vives, Xavier, 1985. "On the efficiency of Bertrand and Cournot equilibria with product differentation," Journal of Economic Theory, Elsevier, vol. 36(1), pages 166-175, June.
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  10. 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.
  11. 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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  14. Puu, T., 1998. "The chaotic duopolists revisited," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 385-394, January.
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  16. Pei-Cheng Liao, 2008. "A Note On Market Coverage In Vertical Differentiation Models With Fixed Costs," Bulletin of Economic Research, Wiley Blackwell, vol. 60(1), pages 27-44, 01.
  17. Motta, Massimo, 1993. "Endogenous Quality Choice: Price vs. Quantity Competition," Journal of Industrial Economics, Wiley Blackwell, vol. 41(2), pages 113-31, June.
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  19. 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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