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Dynamic Duopoly with Congestion Effects

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  • Didier Laussel
  • Maxime de Montmarin
  • Ngo Van Long

    ()

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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Bibliographic Info

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

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References

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  1. Karp, Larry, 1996. "Depreciation erodes the Coase Conjecture," European Economic Review, Elsevier, vol. 40(2), pages 473-490, February.
  2. GRILO, Isabel & SHY, Oz & THISSE, Jacques-François, . "Price competition when consumer behavior is characterized by conformity or vanity," CORE Discussion Papers RP -1518, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Léonard,Daniel & Long,Ngo van, 1992. "Optimal Control Theory and Static Optimization in Economics," Cambridge Books, Cambridge University Press, number 9780521331586, October.
  4. d'ASPREMONT, Claude & GABSZEWICZ, Jean J. & THISSE, Jacques-François, . "On Hotelling's "Stability in competition"," CORE Discussion Papers RP -385, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  5. Scotchmer, Suzanne, 1985. "Profit-maximizing clubs," Journal of Public Economics, Elsevier, vol. 27(1), pages 25-45, June.
  6. Driskill, Robert, 2001. "Durable goods oligopoly," International Journal of Industrial Organization, Elsevier, vol. 19(3-4), pages 391-413, March.
  7. Dockner,Engelbert J. & Jorgensen,Steffen & Long,Ngo Van & Sorger,Gerhard, 2000. "Differential Games in Economics and Management Science," Cambridge Books, Cambridge University Press, number 9780521637329, October.
  8. Toker Doganoglu, 2000. "Dynamic Price Competition with Persistent Consumer Tastes," Econometric Society World Congress 2000 Contributed Papers 1442, Econometric Society.
  9. Drew Fudenberg & Jean Tirole, 1991. "Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262061414.
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Citations

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Cited by:
  1. Laussel, Didier & Resende, Joana, 2014. "Dynamic price competition in aftermarkets with network effects," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 106-118.
  2. 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.
  3. Griva, Krina & Vettas, Nikolaos, 2011. "Price competition in a differentiated products duopoly under network effects," Information Economics and Policy, Elsevier, vol. 23(1), pages 85-97, March.
  4. Hilli, Amal & Laussel, Didier & Van Long, Ngo, 2013. "Large shareholders, monitoring, and ownership dynamics: Toward pure managerial firms?," Journal of Economic Dynamics and Control, Elsevier, vol. 37(3), pages 666-679.
  5. Kurt R. Brekke & Roberto Cellini & Luigi Siciliani & Odd Rune Straume, 2010. "Competition and Quality in Regulated Markets with Sluggish Demand," CESifo Working Paper Series 2922, CESifo Group Munich.
  6. Matsumura, Toshihiro & Matsushima, Noriaki, 2007. "Congestion-reducing investments and economic welfare in a Hotelling model," Economics Letters, Elsevier, vol. 96(2), pages 161-167, August.
  7. Brekke, Kurt R. & Cellini, Roberto & Siciliani, Luigi & Straume, Odd Rune, 2010. "Competition and quality in health care markets: A differential-game approach," Journal of Health Economics, Elsevier, vol. 29(4), pages 508-523, July.

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