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Equilibria in Bottleneck Games

Author

Listed:
  • Ryo Kawasaki
  • Hideo Konishi

    (Boston College)

  • Junki Yukawa

Abstract

This paper introduces a bottleneck game with finite sets of commuters and departing time slots as an extension of congestion games by Milchtaich (1996). 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, Le Breton, and Weber, 1997a).

Suggested Citation

  • Ryo Kawasaki & Hideo Konishi & Junki Yukawa, 2018. "Equilibria in Bottleneck Games," Boston College Working Papers in Economics 945, Boston College Department of Economics.
    • Handle: RePEc:boc:bocoec:945
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    References listed on IDEAS

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    1. Gordon F. Newell, 1987. "The Morning Commute for Nonidentical Travelers," Transportation Science, INFORMS, vol. 21(2), pages 74-88, May.
    2. 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.
    3. Arnott, Richard & de Palma, Andre & Lindsey, Robin, 1990. "Economics of a bottleneck," Journal of Urban Economics, Elsevier, vol. 27(1), pages 111-130, January.
    4. Hideo Konishi, 2004. "Uniqueness of User Equilibrium in Transportation Networks with Heterogeneous Commuters," Transportation Science, INFORMS, vol. 38(3), pages 315-330, August.
    5. 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.
    6. Holzman, Ron & Law-Yone, Nissan, 1997. "Strong Equilibrium in Congestion Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 85-101, October.
    7. 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.
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    More about this item

    Keywords

    congestion game; bottleneck model; Nash equlibrium; strong equilibrium; equivalence; existence;
    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

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