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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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    Citations

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    Cited by:

    1. Cellini, Roberto & Brekke, Kurt Richard & Siciliani, Luigi, 2008. "Competition and quality in regulated markets with sluggish demand," CEPR Discussion Papers 6938, C.E.P.R. Discussion Papers.
    2. Didier Laussel & Ngo Van Long, 2012. "Vertical Disintegration: A Dynamic Markovian Approach," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 21(3), pages 745-771, September.
    3. Didier Laussel & Ngo V. Long & Joana Resende, 2020. "The curse of knowledge: having access to customer information can reduce monopoly profits," RAND Journal of Economics, RAND Corporation, vol. 51(3), pages 650-675, September.
    4. Bruno Jullien & Alessandro Pavan & Marc Rysman, 2021. "Two-sided markets, pricing, and network effects," Post-Print hal-03828345, HAL.
    5. 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.
    6. 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.
    7. 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.
    8. Laussel, Didier & Long, Ngo Van & Resende, Joana, 2020. "Quality and price personalization under customer recognition: A dynamic monopoly model with contrasting equilibria," Journal of Economic Dynamics and Control, Elsevier, vol. 114(C).
    9. 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.
    10. 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.
    11. 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.
    12. 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.
    13. Raúl Bajo-Buenestado, 2021. "Market prices, spatial distribution of consumers and firms’ optimal locations in a linear city," Empirical Economics, Springer, vol. 61(1), pages 443-467, July.
    14. Didier Laussel & Ngo Van Long & Joana Resende, 2019. "Quality and Price Personalization under Customer Recognition: A Dynamic Monopoly Model," CIRANO Working Papers 2019s-03, CIRANO.
    15. Laussel, Didier & Resende, Joana, 2014. "Dynamic price competition in aftermarkets with network effects," Journal of Mathematical Economics, Elsevier, vol. 50(C), pages 106-118.
    16. 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.
    17. 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.

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    More about this item

    Keywords

    duopoly; differential games; Markov perfect equilibrium; duopole; jeux différentiels; équilibre markovien parfait;
    All these keywords.

    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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