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Uniqueness of User Equilibrium in Transportation Networks with Heterogeneous Commuters

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Author Info

  • Hideo Konishi

    ()
    (Boston College)

Abstract

This paper discusses uniqueness and efficiency of user equilibrium in transportation networks with heterogeneous commuters. Daganzo (1983, Transportation Science) proved the uniqueness of (stochastic) user equilibrium when commuters have heterogeneous tastes over possible paths but identical disutility functions from time costs. We first show, by example, that his result may not apply in general networks if disutility functions are allowed to differ. However, for "simple" transportation networks, we can show that user equilibrium is always unique and weakly Pareto efficient (cf. the Braess example) for a general class of utility functions. We investigate if this result applies to more general networks. We also show that user equilibrium is unique in a dynamic bottleneck model with a simple network. We discuss an interesting relationship between the following two problems: the existence of user equilibrium in a finite model and the uniqueness of user equilibrium in a continuum model. In the appendix, we also provide a proof of a slightly generalized version of Daganzo's theorem.

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Bibliographic Info

Paper provided by Boston College Department of Economics in its series Boston College Working Papers in Economics with number 494.

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Length: 57 pages
Date of creation: 14 Mar 2001
Date of revision: 14 Nov 2002
Publication status: Published, Transportation Science, 38, 315-330, 2004
Handle: RePEc:boc:bocoec:494

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Postal: Boston College, 140 Commonwealth Avenue, Chestnut Hill MA 02467 USA
Phone: 617-552-3670
Fax: +1-617-552-2308
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Web page: http://fmwww.bc.edu/EC/
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Related research

Keywords: transportation network; user equilibrium; heterogeneous commuters; uniqueness; efficiency; bottleneck model; game theory;

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References

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  1. Takatoshi Tabuchi & Dao-Zhi Zeng, 2000. "Stability of Spatial Equilibrium," CIRJE F-Series CIRJE-F-79, CIRJE, Faculty of Economics, University of Tokyo.
  2. Le Breton, M. & Weber, S., 1995. "Strong Equilibrium in a Model with Partial Rivalry," G.R.E.Q.A.M. 95a07, Universite Aix-Marseille III.
  3. Verhoef, E.T. & Small, K.A., 1999. "Product Differentiation on Roads Second-Best Congestion Pricing with Heterogeneity under Public and Private Ownership," Papers 99-00-01, California Irvine - School of Social Sciences.
  4. Richard Arnott & An Yan, 2000. "The Two-Mode Problem: Second-Best Pricing and Capacity," Boston College Working Papers in Economics 474, Boston College Department of Economics.
  5. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-60, May.
  6. Small, Kenneth & Yan, Jia, 2000. "The Value of "Value Pricing" of Roads: Second-Best Pricing and Product Differentiation," Discussion Papers dp-00-08, Resources For the Future.
  7. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1997. "Equilibria in a Model with Partial Rivalry," Journal of Economic Theory, Elsevier, vol. 72(1), pages 225-237, January.
  8. 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.
  9. Milchtaich, Igal, 1996. "Congestion Games with Player-Specific Payoff Functions," Games and Economic Behavior, Elsevier, vol. 13(1), pages 111-124, March.
  10. Thomas Quint & Martin Shubik, 1994. "A Model of Migration," Cowles Foundation Discussion Papers 1088, Cowles Foundation for Research in Economics, Yale University.
  11. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1992. "Route choice with heterogeneous drivers and group-specific congestion costs," Regional Science and Urban Economics, Elsevier, vol. 22(1), pages 71-102, March.
  12. Kraus, Marvin & Yoshida, Yuichiro, 2002. "The Commuter's Time-of-Use Decision and Optimal Pricing and Service in Urban Mass Transit," Journal of Urban Economics, Elsevier, vol. 51(1), pages 170-195, January.
  13. Konishi, Hideo & Le Breton, Michel & Weber, Shlomo, 1997. "Pure Strategy Nash Equilibrium in a Group Formation Game with Positive Externalities," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 161-182, October.
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Citations

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Cited by:
  1. Berliant, Marcus, 2011. "Repeated Commuting," MPRA Paper 28979, University Library of Munich, Germany.
  2. Holzman, Ron & Law-yone (Lev-tov), Nissan, 2003. "Network structure and strong equilibrium in route selection games," Mathematical Social Sciences, Elsevier, vol. 46(2), pages 193-205, October.
  3. Clifford Winston & Jia Yan, 2008. "US Highway Privatization and Heterogeneous Preferences," Working Papers 2008-20, School of Economic Sciences, Washington State University.
  4. Igal Milchtaich, 2003. "Topological Conditions for Uniqueness of Equilibrium in Networks," Working Papers 2003-01, Department of Economics, Bar-Ilan University.

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