Stability analysis in a Bertrand duopoly with different product quality and heterogeneous expectations
AbstractWe 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.
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoPaper provided by Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy in its series Discussion Papers with number 2011/122.
Date of creation: 09 Jan 2011
Date of revision:
Bifurcation; Different product quality; Duopoly; Heterogeneous players; Price competition.;
Other versions of this item:
- Luciano Fanti & Luca Gori, 2013. "Stability Analysis in a Bertrand Duopoly with Different Product Quality and Heterogeneous Expectations," Journal of Industry, Competition and Trade, Springer, vol. 13(4), pages 481-501, December.
- 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.
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
- D43 - Microeconomics - - Market Structure and Pricing - - - Oligopoly and Other Forms of Market Imperfection
- L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
- L15 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Information and Product Quality
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-10-15 (All new papers)
- NEP-BEC-2011-10-15 (Business Economics)
- NEP-COM-2011-10-15 (Industrial Competition)
- NEP-IND-2011-10-15 (Industrial Organization)
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- Wauthy, Xavier, 1996.
"Quality Choice in Models of Vertical Differentiation,"
Journal of Industrial Economics,
Wiley Blackwell, vol. 44(3), pages 345-53, September.
- Wauthy, X., 1994. "Quality Choice in Models of Vertical Differentiation," Discussion Papers (IRES - Institut de Recherches Economiques et Sociales) 1994033, Université catholique de Louvain, Institut de Recherches Economiques et Sociales (IRES).
- 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.
- Jean Gabszewicz & Didier Laussel & Ornella Tarola, 2010.
"To acquire, or to compete? An entry dilemma,"
4/10, Sapienza University of Rome, DISS.
- Jean J. GABSZEWICZ & Didier, LAUSSEL & Ornella, TAROLLA, 2008. "To acquire or to compete ? An entry dilemna," Discussion Papers (ECON - DÃ©partement des Sciences Economiques) 2008019, Université catholique de Louvain, Département des Sciences Economiques.
- GABSZEWICZ, Jean & LAUSSEL, Didier & TAROLA, Ornella, 2008. "To acquire, or to compete? An entry dilemna," CORE Discussion Papers 2008027, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
- 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.
- Tramontana, Fabio, 2010. "Heterogeneous duopoly with isoelastic demand function," Economic Modelling, Elsevier, vol. 27(1), pages 350-357, January.
- 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.
- 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.
- 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 107-22, February.
- Fabio Tramontana & Laura Gardini & Tönu Puu, 2008.
"Cournot Duopoly when the Competitors Operate Multiple Production Plants,"
0809, University of Urbino Carlo Bo, Department of Economics, Society & Politics - Scientific Committee - L. Stefanini & G. Travaglini, revised 2008.
- 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.
- 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.
- 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.
- 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.
- Jean Tirole, 1988. "The Theory of Industrial Organization," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262200716.
- Fanti, Luciano & Gori, Luca, 2011.
"The dynamics of a Bertrand duopoly with differentiated products and bounded rational firms revisited,"
33268, University Library of Munich, Germany.
- 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.
- 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.
- 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.
- 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.
- Puu, T., 1998. "The chaotic duopolists revisited," Journal of Economic Behavior & Organization, Elsevier, vol. 33(3-4), pages 385-394, January.
- 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.
- Motta, Massimo, 1993. "Endogenous Quality Choice: Price vs. Quantity Competition," Journal of Industrial Economics, Wiley Blackwell, vol. 41(2), pages 113-31, June.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: ().
If references are entirely missing, you can add them using this form.