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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.

Suggested Citation

  • Fanti, Luciano & Gori, Luca, 2011. "Stability analysis in a Bertrand duopoly with different product quality and heterogeneous expectations," MPRA Paper 33480, University Library of Munich, Germany.
  • Handle: RePEc:pra:mprapa:33480
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    References listed on IDEAS

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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 345-353, September.
    2. 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.
    3. Avinash Dixit, 1979. "A Model of Duopoly Suggesting a Theory of Entry Barriers," Bell Journal of Economics, The RAND Corporation, vol. 10(1), pages 20-32, Spring.
    4. 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.
    5. 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.
    6. Motta, Massimo, 1993. "Endogenous Quality Choice: Price vs. Quantity Competition," Journal of Industrial Economics, Wiley Blackwell, vol. 41(2), pages 113-131, June.
    7. 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.
    8. Puu, T., 1998. "The chaotic duopolists revisited," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 385-394, January.
    9. 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.
    10. Chiarella, Carl, 1986. "Perfect foresight models and the dynamic instability problem from a higher viewpoint," Economic Modelling, Elsevier, vol. 3(4), pages 283-292, October.
    11. Bischi, Gian-Italo & Stefanini, Luciano & Gardini, Laura, 1998. "Synchronization, intermittency and critical curves in a duopoly game," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 44(6), pages 559-585.
    12. Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716, January.
    13. Tramontana, Fabio & Gardini, Laura & Puu, Tönu, 2009. "Cournot duopoly when the competitors operate multiple production plants," Journal of Economic Dynamics and Control, Elsevier, vol. 33(1), pages 250-265, January.
    14. Fanti, Luciano & Gori, Luca, 2012. "The dynamics of a differentiated duopoly with quantity competition," Economic Modelling, Elsevier, vol. 29(2), pages 421-427.
    15. R. D. Theocharis, 1960. "On the Stability of the Cournot Solution on the Oligopoly Problem," Review of Economic Studies, Oxford University Press, vol. 27(2), pages 133-134.
    16. Jaskold Gabszewicz, J. & Thisse, J. -F., 1979. "Price competition, quality and income disparities," Journal of Economic Theory, Elsevier, vol. 20(3), pages 340-359, June.
    17. Nirvikar Singh & Xavier Vives, 1984. "Price and Quantity Competition in a Differentiated Duopoly," RAND Journal of Economics, The RAND Corporation, vol. 15(4), pages 546-554, Winter.
    18. 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.
    19. 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, January.
    20. 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.
    21. Dixit, Avinash K, 1986. "Comparative Statics for Oligopoly," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 27(1), pages 107-122, February.
    22. 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.
    23. Tramontana, Fabio, 2010. "Heterogeneous duopoly with isoelastic demand function," Economic Modelling, Elsevier, vol. 27(1), pages 350-357, January.
    24. 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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    Keywords

    Bifurcation; Different product quality; Duopoly; Heterogeneous players; Price competition;

    JEL classification:

    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L15 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Information and Product Quality
    • C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium

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