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Dynamic Duopoly with Congestion Effects

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Author Info
Didier Laussel
Maxime de Montmarin
Ngo Van Long ()

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Abstract

We analyze duopolistic competition between horizontally differentiated firms selling durable goods or services subject to congestion. At each point of time, new customers buy one unit of the commodity from one of the firms, by comparing present prices and future congestion rates. We study the linear Markov equilibrium of this game which exists and is unique when firms are not too different. The existence of negative consumption externalities is shown to soften the price competition. Moreover, we show that the firm with the larger capacity has, at the steady state, a larger market share, a higher price, and a lower congestion rate. The price of an entrant decreases gradually after entry, while the price of the incumbent rises. The speed of convergence to the steady state is faster, the stronger is the congestion effect.

On étudie la concurrence entre deux firmes qui vendent des biens ou des services durables sous la condition d'encombrement. À chaque instant, des clients nouveaux achètent une unité du bien, en comparant les prix et les taux d'encombrement futur. On caractérise l'équilibre markovien de ce jeu. L'existence des externalités négatives rend la concurrence moins féroce. On montre que la firme qui a la plus grande capacité a, dans l'état stationnaire, une plus grande part de marché, un prix plus élevé, et un taux d'encombrement plus faible. Le prix du bien d'une nouvelle firme diminue continuellement, tandis que celui de son rival en exercise monte. La vitesse de convergence est une fonction croissante de l'effet d'encombrement.

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Paper provided by CIRANO in its series CIRANO Working Papers with number 2004s-09.

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Date of creation: 01 Feb 2004
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Handle: RePEc:cir:cirwor:2004s-09

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Related research
Keywords: duopoly; differential games; Markov perfect equilibrium; duopole; jeux différentiels; équilibre markovien parfait;

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Find related papers by JEL classification:
C61 - Mathematical and Quantitative Methods - - Mathematical Methods and Programming - - - Optimization Techniques; Programming Models; Dynamic Analysis
D42 - Microeconomics - - Market Structure and Pricing - - - Monopoly
D92 - Microeconomics - - Intertemporal Choice and Growth - - - Intertemporal Firm Choice and Growth, Investment, or Financing
H21 - Public Economics - - Taxation, Subsidies, and Revenue - - - Efficiency; Optimal Taxation
L5 - Industrial Organization - - Regulation and Industrial Policy

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References listed on IDEAS
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.:
  1. Karp, Larry, 1996. "Depreciation erodes the Coase Conjecture," European Economic Review, Elsevier, vol. 40(2), pages 473-490, February. [Downloadable!] (restricted)
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  2. Grilo, Isabel & Shy, Oz & Thisse, Jacques-Francois, 2001. "Price competition when consumer behavior is characterized by conformity or vanity," Journal of Public Economics, Elsevier, vol. 80(3), pages 385-408, June. [Downloadable!] (restricted)
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  3. Scotchmer, Suzanne, 1985. "Profit-maximizing clubs," Journal of Public Economics, Elsevier, vol. 27(1), pages 25-45, June. [Downloadable!] (restricted)
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Cited by:
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  1. Steffen Jørgensen & Georges Zaccour, 2007. "Developments in differential game theory and numerical methods: economic and management applications," Computational Management Science, Springer, vol. 4(2), pages 159-181, April. [Downloadable!] (restricted)
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