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On the Existence and Uniqueness of Equilibrium in the Bottleneck Model with Atomic Users

Author

Listed:
  • Hugo E. Silva

    (Department of Spatial Economics, Faculty of Economics and Business Administration, Free University, De Boelelaan 1105, 1081 HV Amsterdam, Netherlands - affiliation inconnue)

  • Robin Lindsey

    (UBC - University of British Columbia)

  • André de Palma

    (ENS Cachan - École normale supérieure - Cachan, X-DEP-ECO - Département d'Économie de l'École Polytechnique - X - École polytechnique)

  • Vincent A.C. van den Berg

    (Tinbergen Institute - Tinbergen Institute)

Abstract

This paper investigates the existence and uniqueness of equilibrium in the Vickrey bottleneck model when each user controls a positive fraction of total traffic. Users simultaneously choose departure schedules for their vehicle fleets. Each user internalizes the congestion cost that each of its vehicles imposes on other vehicles in its fleet. We establish three results. First, a pure strategy Nash equilibrium (PSNE) may not exist. Second, if a PSNE does exist, identical users may incur appreciably different equilibrium costs. Finally, a multiplicity of PSNE can exist in which no queuing occurs but departures begin earlier or later than in the system optimum. The order in which users depart can be suboptimal as well. Nevertheless, by internalizing self-imposed congestion costs individual users can realize much, and possibly all, of the potential cost savings from either centralized traffic control or time-varying congestion tolls.

Suggested Citation

  • Hugo E. Silva & Robin Lindsey & André de Palma & Vincent A.C. van den Berg, 2015. "On the Existence and Uniqueness of Equilibrium in the Bottleneck Model with Atomic Users," Working Papers hal-01149107, HAL.
  • Handle: RePEc:hal:wpaper:hal-01149107
    DOI: 10.2139/ssrn.2461180
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-01149107
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    Cited by:

    1. Lindsey, Robin & de Palma, André & Silva, Hugo E., 2019. "Equilibrium in a dynamic model of congestion with large and small users," Transportation Research Part B: Methodological, Elsevier, vol. 124(C), pages 82-107.
    2. Jiang, Changmin & Zhang, Anming, 2015. "Airport congestion pricing and terminal investment: Effects of terminal congestion, passenger types, and concessionsAuthor-Name: Wan, Yulai," Transportation Research Part B: Methodological, Elsevier, vol. 82(C), pages 91-113.
    3. Ren-Yong Guo & Hai Yang & Hai-Jun Huang, 2018. "Are We Really Solving the Dynamic Traffic Equilibrium Problem with a Departure Time Choice?," Transportation Science, INFORMS, vol. 52(3), pages 603-620, June.
    4. Amirgholy, Mahyar & Shahabi, Mehrdad & Gao, H. Oliver, 2017. "Optimal design of sustainable transit systems in congested urban networks: A macroscopic approach," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 103(C), pages 261-285.
    5. Li, Zhi-Chun & Huang, Hai-Jun & Yang, Hai, 2020. "Fifty years of the bottleneck model: A bibliometric review and future research directions," Transportation Research Part B: Methodological, Elsevier, vol. 139(C), pages 311-342.
    6. André de Palma & Claude LefÈvre, 2018. "Bottleneck models and departure time problems," Working Papers hal-01581519, HAL.
    7. Verhoef, Erik T. & Silva, Hugo E., 2017. "Dynamic equilibrium at a congestible facility under market power," Transportation Research Part B: Methodological, Elsevier, vol. 105(C), pages 174-192.
    8. Federico Boffa & Alessandro Fedele & Alberto Iozzi, 2020. "Congestion and Incentives in the Age of Driverless Fleets," BEMPS - Bozen Economics & Management Paper Series BEMPS67, Faculty of Economics and Management at the Free University of Bozen.

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    2. Silva, Hugo E. & Verhoef, Erik T. & van den Berg, Vincent A.C., 2014. "Airlines’ strategic interactions and airport pricing in a dynamic bottleneck model of congestion," Journal of Urban Economics, Elsevier, vol. 80(C), pages 13-27.
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    More about this item

    Keywords

    Bottleneck model; Large users; Atomic users; Existence of Equilibrium; Uniqueness of Equilibrium;
    All these keywords.

    JEL classification:

    • L9 - Industrial Organization - - Industry Studies: Transportation and Utilities
    • R4 - Urban, Rural, Regional, Real Estate, and Transportation Economics - - Transportation Economics
    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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