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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.

Suggested Citation

  • Hideo Konishi, 2001. "Uniqueness of User Equilibrium in Transportation Networks with Heterogeneous Commuters," Boston College Working Papers in Economics 494, Boston College Department of Economics, revised 14 Nov 2002.
  • Handle: RePEc:boc:bocoec:494
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    References listed on IDEAS

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    Cited by:

    1. Berliant, Marcus, 2011. "Repeated Commuting," MPRA Paper 28979, University Library of Munich, Germany.
    2. André De Palma & Stef Proost & Ravi Seshadri & Moshe Ben-Akiva, 2016. "Tolls Versus Mobility Permits: A Comparative Analysis," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01397582, HAL.
    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, Bar-Ilan University, Department of Economics.
    5. 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.
    6. Berliant, Marcus, 2017. "Commuting and internet traffic congestion," MPRA Paper 77378, University Library of Munich, Germany.

    More about this item

    Keywords

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

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • R40 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics - - - General
    • R41 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics - - - Transportation: Demand, Supply, and Congestion; Travel Time; Safety and Accidents; Transportation Noise

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