article

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

Authors:

André de Palma,

Vincent A. C. van den BergAuthors Info & Claims

Transportation Science, Volume 51, Issue 3

Pages 863 - 881

https://doi.org/10.1287/trsc.2016.0672

Published: 01 August 2017 Publication History

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.

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Cited By

Long JYang HSzeto W(2022)Departure Time Choice Equilibrium and Tolling Strategies for a Bottleneck with Stochastic CapacityTransportation Science10.1287/trsc.2021.103956:1(79-102)Online publication date: 1-Jan-2022
https://dl.acm.org/doi/10.1287/trsc.2021.1039
Shao QCheung MHuang J(2019)Multimedia Crowdsourcing With Bounded Rationality: A Cognitive Hierarchy PerspectiveIEEE Journal on Selected Areas in Communications10.1109/JSAC.2019.291644837:7(1478-1488)Online publication date: 14-Jun-2019
https://dl.acm.org/doi/10.1109/JSAC.2019.2916448
Guo RYang HHuang H(2018)Are We Really Solving the Dynamic Traffic Equilibrium Problem with a Departure Time Choice?Transportation Science10.1287/trsc.2017.076452:3(603-620)Online publication date: 1-Jun-2018
https://dl.acm.org/doi/10.1287/trsc.2017.0764

Index Terms

On the Existence and Uniqueness of Equilibrium in the Bottleneck Model with Atomic Users
1. Applied computing
  1. Enterprise computing
2. Theory of computation
  1. Design and analysis of algorithms
    1. Mathematical optimization
  2. Theory and algorithms for application domains
    1. Machine learning theory
      1. Reinforcement learning
        Sequential decision making

Index terms have been assigned to the content through auto-classification.

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Published In

cover image Transportation Science

Transportation Science Volume 51, Issue 3

August 2017

239 pages

ISSN:1526-5447

Issue’s Table of Contents

Publisher

INFORMS

Linthicum, MD, United States

Publication History

Published: 01 August 2017

Accepted: 25 November 2015

Received: 14 October 2014

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Cited By

Long JYang HSzeto W(2022)Departure Time Choice Equilibrium and Tolling Strategies for a Bottleneck with Stochastic CapacityTransportation Science10.1287/trsc.2021.103956:1(79-102)Online publication date: 1-Jan-2022
https://dl.acm.org/doi/10.1287/trsc.2021.1039
Shao QCheung MHuang J(2019)Multimedia Crowdsourcing With Bounded Rationality: A Cognitive Hierarchy PerspectiveIEEE Journal on Selected Areas in Communications10.1109/JSAC.2019.291644837:7(1478-1488)Online publication date: 14-Jun-2019
https://dl.acm.org/doi/10.1109/JSAC.2019.2916448
Guo RYang HHuang H(2018)Are We Really Solving the Dynamic Traffic Equilibrium Problem with a Departure Time Choice?Transportation Science10.1287/trsc.2017.076452:3(603-620)Online publication date: 1-Jun-2018
https://dl.acm.org/doi/10.1287/trsc.2017.0764

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