The dynamics of a Bertrand duopoly with differentiated products and bounded rational firms revisited
AbstractWe revisit the study of the dynamics of a duopoly game à la Bertrand with horizontal product differentiation and bounded rational firms analysed by Zhang et al. (2009), (Zhang, J., Da, Q., Wang, Y., 2009. The dynamics of Bertrand model with bounded rationality. Chaos, Solitons and Fractals 39, 2048–2055), by introducing sound microeconomic foundations. We study how an increase in the relative degree of product differentiation affects the stability of the unique positive Bertrand-Nash equilibrium, in the case of both linear and non-linear costs. We show that an increase in either the degree of substitutability or complementarity between goods of different variety may destabilise the equilibrium of the two-dimensional system through a period-doubling bifurcation. Moreover, by using numerical simulations (i.e., phase portraits, sensitive dependence on initial conditions and Lyapunov exponents), we find that a “quasi-periodic” route to chaos and a large gamma of strange attractors for the cases of both substitutability and complementarity can occur.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 33268.
Date of creation: 09 Sep 2011
Date of revision:
Bifurcation; Chaos; Differentiated products; Duopoly; Price competition;
Other versions of this item:
- 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.
- L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets
- D43 - Microeconomics - - Market Structure and Pricing - - - Oligopoly and Other Forms of Market Imperfection
- C62 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Existence and Stability Conditions of Equilibrium
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-09-16 (All new papers)
- NEP-BEC-2011-09-16 (Business Economics)
- NEP-COM-2011-09-16 (Industrial Competition)
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.:
- 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.
- Qiu, Larry D., 1997. "On the Dynamic Efficiency of Bertrand and Cournot Equilibria," Journal of Economic Theory, Elsevier, vol. 75(1), pages 213-229, July.
- Ghosh, Arghya & Mitra, Manipushpak, 2010. "Comparing Bertrand and Cournot in mixed markets," Economics Letters, Elsevier, vol. 109(2), pages 72-74, November.
- Häckner, Jonas, 1999.
"A Note on Price and Quantity Competition in Differentiated Oligopolies,"
Research Papers in Economics
1999:9, Stockholm University, Department of Economics.
- Hackner, Jonas, 2000. "A Note on Price and Quantity Competition in Differentiated Oligopolies," Journal of Economic Theory, Elsevier, vol. 93(2), pages 233-239, August.
- 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.
- Luciano Fanti & Nicola Meccheri, 2010.
"The Cournot-Bertrand Profit Differential in a Differentiated Duopoly with Unions and Labour Decreasing Returns,"
Working Paper Series
36_10, The Rimini Centre for Economic Analysis.
- Luciano Fanti & Nicola Meccheri, 2011. "The Cournot-Bertrand profit differential in a differentiated duopoly with unions and labour decreasing returns," Economics Bulletin, AccessEcon, vol. 31(1), pages 233-244.
- Luciano Fanti & Nicola Meccheri, 2010. "The Cournot-Bertrand profit differential in a differentiated duopoly with unions and labour decreasing returns," Discussion Papers 2010/107, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
- Medio,Alfredo & Gallo,Giampaolo, 1995. "Chaotic Dynamics," Cambridge Books, Cambridge University Press, number 9780521484619, December.
- Lopez, Monica Correa & Naylor, Robin A., 2004. "The Cournot-Bertrand profit differential: A reversal result in a differentiated duopoly with wage bargaining," European Economic Review, Elsevier, vol. 48(3), pages 681-696, June.
- 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.
- Tramontana, Fabio, 2010. "Heterogeneous duopoly with isoelastic demand function," Economic Modelling, Elsevier, vol. 27(1), pages 350-357, January.
- Fanti, Luciano & Gori, Luca, 2011.
"Stability analysis in a Bertrand duopoly with different product quality and heterogeneous expectations,"
33480, University Library of Munich, Germany.
- 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.
- Luciano Fanti & Luca Gori, 2011. "Stability analysis in a Bertrand duopoly with different product quality and heterogeneous expectations," Discussion Papers 2011/122, Dipartimento di Economia e Management (DEM), University of Pisa, Pisa, Italy.
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