IDEAS home Printed from
MyIDEAS: Login to save this article or follow this journal

Vickrey's model of traffic congestion discretized

  • Otsubo, Hironori
  • Rapoport, Amnon

Vickrey's seminal analysis of urban traffic congestion assumes a continuum of commuters acting selfishly and a continuous strategy space. We propose a discrete version of his model that assumes a finite number of commuters and a discrete strategy space. We then present an algorithm for numerically computing a symmetric mixed-strategy equilibrium solution for the discrete model and compare it with the deterministic equilibrium solution for the continuous model due to Arnott et al. [Arnott, R., de Palma, A., Lindsey, R., 1990. Economics of a bottleneck. Journal of Urban Economics 27(1), 111-130]. We report significant discrepancies in travel costs and distributions of departure time between the two solutions that slowly decrease as the number of commuters increases. We then propose and exemplify two extensions of the discrete model that allow for an uncertain number of commuters and an alternative mode of transportation not subject to congestion.

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.

File URL:
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Article provided by Elsevier in its journal Transportation Research Part B: Methodological.

Volume (Year): 42 (2008)
Issue (Month): 10 (December)
Pages: 873-889

in new window

Handle: RePEc:eee:transb:v:42:y:2008:i:10:p:873-889
Contact details of provider: Web page:

Order Information: Postal:

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.:

as in new window
  1. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1999. "Information and time-of-usage decisions in the bottleneck model with stochastic capacity and demand," European Economic Review, Elsevier, vol. 43(3), pages 525-548, March.
  2. Stein, William E. & Rapoport, Amnon & Seale, Darryl A. & Zhang, Hongtao & Zwick, Rami, 2007. "Batch queues with choice of arrivals: Equilibrium analysis and experimental study," Games and Economic Behavior, Elsevier, vol. 59(2), pages 345-363, May.
  3. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, June.
  4. Small, Kenneth A, 1982. "The Scheduling of Consumer Activities: Work Trips," American Economic Review, American Economic Association, vol. 72(3), pages 467-79, June.
  5. Roger B. Myerson, 1994. "Population Uncertainty and Poisson Games," Discussion Papers 1102R, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  6. J. Swarthout & Mark Walker, 2009. "Discrete implementation of the Groves–Ledyard mechanism," Review of Economic Design, Springer, vol. 13(1), pages 101-114, April.
  7. Baye, M.R. & Kovenock, D., 1993. "The Solution to the Tullock Rent-Seeking Game When R > 2: Mixed Strategy Equilibria and Mean Dissipation Rates," Papers 9368, Tilburg - Center for Economic Research.
  8. Daniel, Joseph I., 2001. "Distributional Consequences of Airport Congestion Pricing," Journal of Urban Economics, Elsevier, vol. 50(2), pages 230-258, September.
  9. Dasgupta, Partha & Maskin, Eric, 1986. "The Existence of Equilibrium in Discontinuous Economic Games, I: Theory," Review of Economic Studies, Wiley Blackwell, vol. 53(1), pages 1-26, January.
  10. Rapoport, Amnon & Stein, William E. & Parco, James E. & Seale, Darryl A., 2004. "Equilibrium play in single-server queues with endogenously determined arrival times," Journal of Economic Behavior & Organization, Elsevier, vol. 55(1), pages 67-91, September.
  11. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1990. "Economics of a bottleneck," Journal of Urban Economics, Elsevier, vol. 27(1), pages 111-130, January.
  12. Kene Boun My & Laurent Denant-Boèmont & Frédéric Koessler & Marc Willinger & Anthony Ziegelmeyer, 2006. "Road Traffic Congestion and Public Information: An Experimental Investigation," Papers on Strategic Interaction 2006-20, Max Planck Institute of Economics, Strategic Interaction Group.
  13. Smith, M. J., 1983. "The existence and calculation of traffic equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 17(4), pages 291-303, August.
  14. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-60, May.
  15. Wilson, Paul W., 1988. "Wage variation resulting from staggered work hours," Journal of Urban Economics, Elsevier, vol. 24(1), pages 9-26, July.
  16. Xi Zou & David Levinson, 2006. "A Multi-Agent Congestion and Pricing Model," Working Papers 200605, University of Minnesota: Nexus Research Group.
  17. Levinson, David, 2005. "Micro-foundations of congestion and pricing: A game theory perspective," Transportation Research Part A: Policy and Practice, Elsevier, vol. 39(7-9), pages 691-704.
  18. Darryl Seale & James Parco & William Stein & Amnon Rapoport, 2005. "Joining a Queue or Staying Out: Effects of Information Structure and Service Time on Arrival and Staying Out Decisions," Experimental Economics, Springer, vol. 8(2), pages 117-144, June.
  19. Theodore Groves & John Ledyard, 1976. "Optimal Allocation of Public Goods: A Solution to the 'Free Rider Problem'," Discussion Papers 144, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
  20. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1993. "A Structural Model of Peak-Period Congestion: A Traffic Bottleneck with Elastic Demand," American Economic Review, American Economic Association, vol. 83(1), pages 161-79, March.
Full references (including those not matched with items on IDEAS)

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

When requesting a correction, please mention this item's handle: RePEc:eee:transb:v:42:y:2008:i:10:p:873-889. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei)

If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

If references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.

If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.

Please note that corrections may take a couple of weeks to filter through the various RePEc services.

This information is provided to you by IDEAS at the Research Division of the Federal Reserve Bank of St. Louis using RePEc data.