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Price competition, free entry, and welfare in congested markets


  • Melo, Emerson


In this paper we study the problem of price competition and free entry in congested markets. In particular, we consider a network with multiple origins and a common destination node, where each link is owned by a firm that sets prices in order to maximize profits, whereas users want to minimize the total cost they face, which is given by the congestion cost plus the prices set by firms. In this environment, we introduce the notion of Markovian Traffic Equilibrium to establish the existence and uniqueness of a pure strategy price equilibrium, without assuming that the demand functions are concave nor imposing particular functional forms for the latency functions. We derive explicit conditions to guarantee existence and uniqueness of equilibria. Given this existence and uniqueness result, we apply our framework to study entry decisions and welfare, and establish that in congested markets with free entry, the number of firms exceeds the social optimum.

Suggested Citation

  • Melo, Emerson, 2014. "Price competition, free entry, and welfare in congested markets," Games and Economic Behavior, Elsevier, vol. 83(C), pages 53-72.
  • Handle: RePEc:eee:gamebe:v:83:y:2014:i:c:p:53-72
    DOI: 10.1016/j.geb.2013.10.006

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    References listed on IDEAS

    1. Fisk, Caroline, 1980. "Some developments in equilibrium traffic assignment," Transportation Research Part B: Methodological, Elsevier, vol. 14(3), pages 243-255, September.
    2. De Borger, B. & Proost, S. & Van Dender, K., 2005. "Congestion and tax competition in a parallel network," European Economic Review, Elsevier, vol. 49(8), pages 2013-2040, November.
    3. Caplin, Andrew & Nalebuff, Barry, 1991. "Aggregation and Imperfect Competition: On the Existence of Equilibrium," Econometrica, Econometric Society, vol. 59(1), pages 25-59, January.
    4. Anderson, Simon P & de Palma, Andre & Nesterov, Yurii, 1995. "Oligopolistic Competition and the Optimal Provision of Products," Econometrica, Econometric Society, vol. 63(6), pages 1281-1301, November.
    5. De Borger, B. & Dunkerley, F. & Proost, S., 2007. "Strategic investment and pricing decisions in a congested transport corridor," Journal of Urban Economics, Elsevier, vol. 62(2), pages 294-316, September.
    6. N. Gregory Mankiw & Michael D. Whinston, 1986. "Free Entry and Social Inefficiency," RAND Journal of Economics, The RAND Corporation, vol. 17(1), pages 48-58, Spring.
    7. Engel Eduardo M & Fischer Ronald & Galetovic Alexander, 2004. "Toll Competition Among Congested Roads," The B.E. Journal of Economic Analysis & Policy, De Gruyter, vol. 4(1), pages 1-21, March.
    8. Israel Luski, 1976. "On Partial Equilibrium in a Queuing System with Two Servers," Review of Economic Studies, Oxford University Press, vol. 43(3), pages 519-525.
    9. Pio Baake & Kay Mitusch, 2007. "Competition with Congestible Networks," Journal of Economics, Springer, vol. 91(2), pages 151-176, June.
    10. Levhari, David & Luski, Israel, 1978. "Duopoly pricing and waiting lines," European Economic Review, Elsevier, vol. 11(1), pages 17-35, February.
    11. Gérard P. Cachon & Patrick T. Harker, 2002. "Competition and Outsourcing with Scale Economies," Management Science, INFORMS, vol. 48(10), pages 1314-1333, October.
    12. Xavier Vives, 2001. "Oligopoly Pricing: Old Ideas and New Tools," MIT Press Books, The MIT Press, edition 1, volume 1, number 026272040x, January.
    13. Reitman, David, 1991. "Endogenous Quality Differentiation in Congested Markets," Journal of Industrial Economics, Wiley Blackwell, vol. 39(6), pages 621-647, December.
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    More about this item


    Price competition; Networks; Discrete choice; Dynamic programming; Welfare; Entry decisions;

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D43 - Microeconomics - - Market Structure, Pricing, and Design - - - Oligopoly and Other Forms of Market Imperfection
    • L13 - Industrial Organization - - Market Structure, Firm Strategy, and Market Performance - - - Oligopoly and Other Imperfect Markets


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