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.
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Bibliographic InfoPaper provided by University Library of Munich, Germany in its series MPRA Paper with number 33480.
Date of creation: 17 Sep 2011
Date of revision:
Bifurcation; Different product quality; Duopoly; Heterogeneous players; Price competition;
Other versions of this item:
- 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.
- 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
- 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
This paper has been announced in the following NEP Reports:
- NEP-ALL-2011-09-22 (All new papers)
- NEP-BEC-2011-09-22 (Business Economics)
- NEP-COM-2011-09-22 (Industrial Competition)
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