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Dynamic Duopoly with Congestion Effects

Author

Listed:
  • 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.

Suggested Citation

  • Didier Laussel & Maxime de Montmarin & Ngo Van Long, 2004. "Dynamic Duopoly with Congestion Effects," CIRANO Working Papers 2004s-09, CIRANO.
  • Handle: RePEc:cir:cirwor:2004s-09
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    References listed on IDEAS

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    1. Léonard,Daniel & Long,Ngo van, 1992. "Optimal Control Theory and Static Optimization in Economics," Cambridge Books, Cambridge University Press, number 9780521331586.
    2. Driskill, Robert, 2001. "Durable goods oligopoly," International Journal of Industrial Organization, Elsevier, vol. 19(3-4), pages 391-413, March.
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    4. 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.
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    6. 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.
    7. Karp, Larry, 1996. "Depreciation erodes the Coase Conjecture," European Economic Review, Elsevier, vol. 40(2), pages 473-490, February.
    8. Toker Doganoglu, 2000. "Dynamic Price Competition with Persistent Consumer Tastes," Econometric Society World Congress 2000 Contributed Papers 1442, Econometric Society.
    9. Scotchmer, Suzanne, 1985. "Profit-maximizing clubs," Journal of Public Economics, Elsevier, vol. 27(1), pages 25-45, June.
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    Citations

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    Cited by:

    1. Laussel, Didier & Van Long, Ngo & Resende, Joana, 2015. "Network effects, aftermarkets and the Coase conjecture: A dynamic Markovian approach," International Journal of Industrial Organization, Elsevier, vol. 41(C), pages 84-96.
    2. 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.
    3. Rabah Amir & Jean Gabszewicz & Joana Resende, 2014. "Thematic Clubs and the Supremacy of Network Externalities," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 16(5), pages 706-729, October.
    4. Laussel, Didier & Resende, Joana, 2014. "Dynamic price competition in aftermarkets with network effects," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 106-118.
    5. 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.
    6. 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.
    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.
    8. 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.
    9. Alfredo Garcia & Yue Sun & Joseph Shen, 2014. "Dynamic Platform Competition with Malicious Users," Dynamic Games and Applications, Springer, vol. 4(3), pages 290-308, September.
    10. Brekke, Kurt Richard & Cellini, Roberto & Siciliani, Luigi & Straume, Odd Rune, 2008. "Competition and quality in regulated markets with sluggish demand," CEPR Discussion Papers 6938, C.E.P.R. Discussion Papers.
    11. Ngo Long, 2015. "Dynamic Games Between Firms and Infinitely Lived Consumers: A Review of the Literature," Dynamic Games and Applications, Springer, vol. 5(4), pages 467-492, December.

    More about this item

    Keywords

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

    JEL classification:

    • C61 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Optimization Techniques; Programming Models; Dynamic Analysis
    • D42 - Microeconomics - - Market Structure, Pricing, and Design - - - Monopoly
    • D92 - Microeconomics - - Micro-Based Behavioral Economics - - - Intertemporal Firm Choice, Investment, Capacity, and Financing
    • H21 - Public Economics - - Taxation, Subsidies, and Revenue - - - Efficiency; Optimal Taxation
    • L5 - Industrial Organization - - Regulation and Industrial Policy

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