Fanti, Luciano and Gori, Luca (2011): Stability analysis in a Bertrand duopoly with different product quality and heterogeneous expectations.
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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.
|Item Type:||MPRA Paper|
|Original Title:||Stability analysis in a Bertrand duopoly with different product quality and heterogeneous expectations|
|English Title:||Stability analysis in a Bertrand duopoly with different product quality and heterogeneous expectations|
|Keywords:||Bifurcation; Different product quality; Duopoly; Heterogeneous players; Price competition|
|Subjects:||L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L13 - Oligopoly and Other Imperfect Markets
D - Microeconomics > D4 - Market Structure and Pricing > D43 - Oligopoly and Other Forms of Market Imperfection
L - Industrial Organization > L1 - Market Structure, Firm Strategy, and Market Performance > L15 - Information and Product Quality; Standardization and Compatibility
C - Mathematical and Quantitative Methods > C6 - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling > C62 - Existence and Stability Conditions of Equilibrium
|Depositing User:||Luca Gori|
|Date Deposited:||17. Sep 2011 18:55|
|Last Modified:||16. Feb 2013 05:23|
Agiza, H.N., Elsadany, A.A., 2003. Nonlinear dynamics in the Cournot duopoly game with heterogeneous players. Physica A 320, 512–524.
Agiza, H.N., Elsadany, A.A., 2004. Chaotic dynamics in nonlinear duopoly game with heterogeneous players. Applied Mathematics and Computation 149, 843–860.
Bertrand, J., 1883. Théorie mathématique de la richesse sociale. Journal des Savants 48, 499–508.
Bischi, G.I., Naimzada, A., 1999. Global analysis of a dynamic duopoly game with bounded rationality. Advanced in Dynamics Games and Application, vol. 5. Birkhauser, Basel. Chapter 20.
Cournot, A., 1838. Recherches sur les Principes Mathématiques de la Théorie des Richessess. Paris: Hachette.
Dixit, A.K., 1986. Comparative statics for oligopoly. International Economic Review 27, 107–122.
Fanti, L., Gori, L., 2011. The dynamics of a Bertrand duopoly with differentiated products and bounded rational firms revisited. MPRA Working Paper no. 33268.
Kopel, M., 1996. Simple and complex adjustment dynamics in Cournot duopoly models. Chaos, Solitons and Fractals 12, 2031–2048.
Puu, T., 1991. Chaos in duopoly pricing. Chaos, Solitons and Fractals 1, 573–581.
Puu, T., 1998. The chaotic duopolists revisited. Journal of Economic Behavior & Organization 33, 385–394.
Tarola, O., Gabszewicz, J.J.. Laussel, D., 2011. To acquire, or to compete? An entry dilemma. Journal of Industry, Competition and Trade, forthcoming.
Theocharis R.D. 1960. On the stability of the Cournot solution on the oligopoly problem. Review of Economic Studies 27, 133–134.
Tramontana, F., 2010. Heterogeneous duopoly with isoelastic demand function. Economic Modelling 27, 350–357.
Zhang, J., Da, Q., Wang, Y., 2007. Analysis of nonlinear duopoly game with heterogeneous players. Economic Modelling 24, 138–148.
Zhang, J., Da, Q., Wang, Y., 2009. The dynamics of Bertrand model with bounded rationality. Chaos, Solitons and Fractals 39, 2048–2055.