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Uniqueness of User Equilibrium in Transportation Networks with Heterogeneous Commuters

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  • 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. Erik T. Verhoef & Kenneth A. Small, 1999. "Product Differentiation on Roads: Second-Best Congestion Pricing with Heterogeneity under Public and Private Ownership," Tinbergen Institute Discussion Papers 99-066/3, Tinbergen Institute.
  2. Thomas Quint & Martin Shubik, 1994. "A Model of Migration," Cowles Foundation Discussion Papers 1088, Cowles Foundation for Research in Economics, Yale University.
  3. 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.
  4. Takatoshi Tabuchi & Dao-Zhi Zeng, 2004. "Stability of Spatial Equilibrium," Journal of Regional Science, Wiley Blackwell, vol. 44(4), pages 641-660.
  5. 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.
  6. 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.
  7. 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.
  8. Milchtaich, Igal, 1996. "Congestion Games with Player-Specific Payoff Functions," Games and Economic Behavior, Elsevier, vol. 13(1), pages 111-124, March.
  9. 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.
  10. 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.
  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. 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.
  13. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-60, May.
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Citations

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Cited by:
  1. Clifford Winston & Jia Yan, 2008. "US Highway Privatization and Heterogeneous Preferences," Working Papers 2008-20, School of Economic Sciences, Washington State University.
  2. Berliant, Marcus, 2011. "Repeated Commuting," MPRA Paper 28979, University Library of Munich, Germany.
  3. 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.
  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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