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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.

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

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

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Handle: RePEc:eee:transb:v:42:y:2008:i:10:p:873-889
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  1. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-60, May.
  2. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1990. "Economics of a bottleneck," Journal of Urban Economics, Elsevier, vol. 27(1), pages 111-130, January.
  3. Small, Kenneth A, 1982. "The Scheduling of Consumer Activities: Work Trips," American Economic Review, American Economic Association, vol. 72(3), pages 467-79, June.
  4. 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.
  5. William E. Stein & Amnon Rapoport & Darryl A. Seale & Hongtao Zhang & Rami Zwick, 2004. "Batch Queues with Choice of Arrivals: Equilibrium Analysis and Experimental Study," Experimental 0411001, EconWPA.
  6. Xi Zou & David Levinson, 2006. "A Multi-Agent Congestion and Pricing Model," Working Papers 200605, University of Minnesota: Nexus Research Group.
  7. 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.
  8. Roger B. Myerson, 1998. "Population uncertainty and Poisson games," International Journal of Game Theory, Springer, vol. 27(3), pages 375-392.
  9. Smith, M. J., 1983. "The existence and calculation of traffic equilibria," Transportation Research Part B: Methodological, Elsevier, vol. 17(4), pages 291-303, August.
  10. 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.
  11. 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.
  12. Groves, Theodore & Ledyard, John O, 1977. "Optimal Allocation of Public Goods: A Solution to the "Free Rider" Problem," Econometrica, Econometric Society, vol. 45(4), pages 783-809, May.
  13. 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.
  14. 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.
  15. Martin J Osborne & Ariel Rubinstein, 2009. "A Course in Game Theory," Levine's Bibliography 814577000000000225, UCLA Department of Economics.
  16. J. Swarthout & Mark Walker, 2009. "Discrete implementation of the Groves–Ledyard mechanism," Review of Economic Design, Springer, vol. 13(1), pages 101-114, April.
  17. Wilson, Paul W., 1988. "Wage variation resulting from staggered work hours," Journal of Urban Economics, Elsevier, vol. 24(1), pages 9-26, July.
  18. 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.
  19. 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.
  20. Daniel, Joseph I., 2001. "Distributional Consequences of Airport Congestion Pricing," Journal of Urban Economics, Elsevier, vol. 50(2), pages 230-258, September.
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