IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v52y2023i3d10.1007_s00182-022-00834-z.html
   My bibliography  Save this article

Equilibria in bottleneck games

Author

Listed:
  • Ryo Kawasaki

    (Tokyo Institute of Technology)

  • Hideo Konishi

    (Boston College)

  • Junki Yukawa

    (Tokyo Institute of Technology)

Abstract

This paper introduces a bottleneck game with finite sets of commuters and departing time slots as an extension of congestion games of Konishi et al. (J Econ Theory 72:225–237, 1997a). After characterizing Nash equilibrium of the game, we provide sufficient conditions for which the equivalence between Nash and strong equilibria holds. Somewhat surprisingly, unlike in congestion games, a Nash equilibrium in pure strategies may often fail to exist, even when players are homogeneous. In contrast, when there is a continuum of atomless players, the existence of a Nash equilibrium and the equivalence between the set of Nash and strong equilibria hold as in congestion games (Konishi et al. 1997a).

Suggested Citation

  • Ryo Kawasaki & Hideo Konishi & Junki Yukawa, 2023. "Equilibria in bottleneck games," International Journal of Game Theory, Springer;Game Theory Society, vol. 52(3), pages 649-685, September.
    • Handle: RePEc:spr:jogath:v:52:y:2023:i:3:d:10.1007_s00182-022-00834-z
    DOI: 10.1007/s00182-022-00834-z
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00182-022-00834-z
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00182-022-00834-z?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to look for a different version below or search for a different version of it.

    Other versions of this item:

    References listed on IDEAS

    as
    1. Hideo Konishi, 2004. "Uniqueness of User Equilibrium in Transportation Networks with Heterogeneous Commuters," Transportation Science, INFORMS, vol. 38(3), pages 315-330, August.
    2. Roberto Cominetti & José Correa & Omar Larré, 2015. "Dynamic Equilibria in Fluid Queueing Networks," Operations Research, INFORMS, vol. 63(1), pages 21-34, February.
    3. Milchtaich, Igal, 1996. "Congestion Games with Player-Specific Payoff Functions," Games and Economic Behavior, Elsevier, vol. 13(1), pages 111-124, March.
    4. Thomas Rivera & Marco Scarsini & Tristan Tomala, 2018. "Efficiency of Correlation in a Bottleneck Game," Working Papers hal-01933853, HAL.
    5. Mark Voorneveld & Peter Borm & Freek Van Megen & Stef Tijs & Giovanni Facchini, 1999. "Congestion Games And Potentials Reconsidered," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 1(03n04), pages 283-299.
    6. SCHMEIDLER, David, 1973. "Equilibrium points of nonatomic games," LIDAM Reprints CORE 146, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Small, Kenneth A., 2015. "The bottleneck model: An assessment and interpretation," Economics of Transportation, Elsevier, vol. 4(1), pages 110-117.
    8. repec:fth:tilbur:9998 is not listed on IDEAS
    9. Vickrey, William S, 1969. "Congestion Theory and Transport Investment," American Economic Review, American Economic Association, vol. 59(2), pages 251-260, May.
    10. Konishi, Hideo & Fishburn, Peter, 1996. "Quasi-linear utility in a discrete choice model," Economics Letters, Elsevier, vol. 51(2), pages 197-200, May.
    11. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1990. "Economics of a bottleneck," Journal of Urban Economics, Elsevier, vol. 27(1), pages 111-130, January.
    12. Carlos F. Daganzo, 1985. "The Uniqueness of a Time-dependent Equilibrium Distribution of Arrivals at a Single Bottleneck," Transportation Science, INFORMS, vol. 19(1), pages 29-37, February.
    13. Michael J. Smith, 1984. "The Existence of a Time-Dependent Equilibrium Distribution of Arrivals at a Single Bottleneck," Transportation Science, INFORMS, vol. 18(4), pages 385-394, November.
    14. Kenneth Small, 2015. "The Bottleneck Model: An Assessment and Interpretation," Working Papers 141506, University of California-Irvine, Department of Economics.
    15. 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.
    16. Gordon F. Newell, 1987. "The Morning Commute for Nonidentical Travelers," Transportation Science, INFORMS, vol. 21(2), pages 74-88, May.
    17. Chris Hendrickson & George Kocur, 1981. "Schedule Delay and Departure Time Decisions in a Deterministic Model," Transportation Science, INFORMS, vol. 15(1), pages 62-77, February.
    18. Holzman, Ron & Law-Yone, Nissan, 1997. "Strong Equilibrium in Congestion Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 85-101, October.
    19. Tobias Harks & Max Klimm & Rolf Möhring, 2013. "Strong equilibria in games with the lexicographical improvement property," International Journal of Game Theory, Springer;Game Theory Society, vol. 42(2), pages 461-482, May.
    20. 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.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Amirgholy, Mahyar & Gao, H. Oliver, 2017. "Modeling the dynamics of congestion in large urban networks using the macroscopic fundamental diagram: User equilibrium, system optimum, and pricing strategies," Transportation Research Part B: Methodological, Elsevier, vol. 104(C), pages 215-237.
    2. 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.
    3. Hideo Konishi, 2004. "Uniqueness of User Equilibrium in Transportation Networks with Heterogeneous Commuters," Transportation Science, INFORMS, vol. 38(3), pages 315-330, August.
    4. Braid, Ralph M., 2018. "Partial peak-load pricing of a transportation bottleneck with homogeneous and heterogeneous values of time," Economics of Transportation, Elsevier, vol. 16(C), pages 29-41.
    5. Yu Nie, 2015. "A New Tradable Credit Scheme for the Morning Commute Problem," Networks and Spatial Economics, Springer, vol. 15(3), pages 719-741, September.
    6. Zhu, Zheng & Li, Xinwei & Liu, Wei & Yang, Hai, 2019. "Day-to-day evolution of departure time choice in stochastic capacity bottleneck models with bounded rationality and various information perceptions," Transportation Research Part E: Logistics and Transportation Review, Elsevier, vol. 131(C), pages 168-192.
    7. Chen, Hongyu & Liu, Yang & Nie, Yu (Marco), 2015. "Solving the step-tolled bottleneck model with general user heterogeneity," Transportation Research Part B: Methodological, Elsevier, vol. 81(P1), pages 210-229.
    8. Ramadurai, Gitakrishnan & Ukkusuri, Satish V. & Zhao, Jinye & Pang, Jong-Shi, 2010. "Linear complementarity formulation for single bottleneck model with heterogeneous commuters," Transportation Research Part B: Methodological, Elsevier, vol. 44(2), pages 193-214, February.
    9. Akamatsu, Takashi & Wada, Kentaro & Iryo, Takamasa & Hayashi, Shunsuke, 2021. "A new look at departure time choice equilibrium models with heterogeneous users," Transportation Research Part B: Methodological, Elsevier, vol. 148(C), pages 152-182.
    10. Nie, Yu (Marco) & Yin, Yafeng, 2013. "Managing rush hour travel choices with tradable credit scheme," Transportation Research Part B: Methodological, Elsevier, vol. 50(C), pages 1-19.
    11. Osawa, Minoru & Fu, Haoran & Akamatsu, Takashi, 2018. "First-best dynamic assignment of commuters with endogenous heterogeneities in a corridor network," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 811-831.
    12. Xiaojuan Yu & Vincent van den Berg & Erik Verhoef, 2019. "Autonomous cars and dynamic bottleneck congestion revisited: how in-vehicle activities determine aggregate travel patterns," Tinbergen Institute Discussion Papers 19-067/VIII, Tinbergen Institute.
    13. Sun, Jian & Wu, Jiyan & Xiao, Feng & Tian, Ye & Xu, Xiangdong, 2020. "Managing bottleneck congestion with incentives," Transportation Research Part B: Methodological, Elsevier, vol. 134(C), pages 143-166.
    14. Robin Lindsey, 2004. "Existence, Uniqueness, and Trip Cost Function Properties of User Equilibrium in the Bottleneck Model with Multiple User Classes," Transportation Science, INFORMS, vol. 38(3), pages 293-314, August.
    15. Kenneth Small, 2015. "The Bottleneck Model: An Assessment and Interpretation," Working Papers 141506, University of California-Irvine, Department of Economics.
    16. Le Breton, Michel & Shapoval, Alexander & Weber, Shlomo, 2021. "A game-theoretical model of the landscape theory," Journal of Mathematical Economics, Elsevier, vol. 92(C), pages 41-46.
    17. Liu, Yang & Nie, Yu (Marco), 2011. "Morning commute problem considering route choice, user heterogeneity and alternative system optima," Transportation Research Part B: Methodological, Elsevier, vol. 45(4), pages 619-642.
    18. Shen, Wei & Zhang, H.M., 2010. "Pareto-improving ramp metering strategies for reducing congestion in the morning commute," Transportation Research Part A: Policy and Practice, Elsevier, vol. 44(9), pages 676-696, November.
    19. Peer, Stefanie & Verhoef, Erik T., 2013. "Equilibrium at a bottleneck when long-run and short-run scheduling preferences diverge," Transportation Research Part B: Methodological, Elsevier, vol. 57(C), pages 12-27.
    20. Guo, Ren-Yong & Yang, Hai & Huang, Hai-Jun & Li, Xinwei, 2018. "Day-to-day departure time choice under bounded rationality in the bottleneck model," Transportation Research Part B: Methodological, Elsevier, vol. 117(PB), pages 832-849.

    More about this item

    Keywords

    Bottleneck game; Nash equilibrium; Strong equilibrium;
    All these keywords.

    JEL classification:

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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:spr:jogath:v:52:y:2023:i:3:d:10.1007_s00182-022-00834-z. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.