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A formula for Nash equilibria in monotone singleton congestion games

Author

Listed:
  • Samir Sbabou

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

  • Hatem Smaoui

    (CEMOI - Centre d'Économie et de Management de l'Océan Indien - UR - Université de La Réunion)

  • Abderrahmane Ziad

    (CREM - Centre de recherche en économie et management - UNICAEN - Université de Caen Normandie - NU - Normandie Université - UR - Université de Rennes - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper provides a simple formula describing all Nash equilibria in monotone symmetric singleton congestion games. Our approach also yields a new and short proof establishing the existence of a Nash equilibrium in this kind of congestion games.

Suggested Citation

  • Samir Sbabou & Hatem Smaoui & Abderrahmane Ziad, 2013. "A formula for Nash equilibria in monotone singleton congestion games," Post-Print halshs-00869876, HAL.
    • Handle: RePEc:hal:journl:halshs-00869876
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    References listed on IDEAS

    as
    1. Voorneveld, M. & Borm, P.E.M. & van Megen, F.J.C. & Tijs, S.H. & Facchini, G., 1999. "Congestion games and potentials reconsidered," Other publications TiSEM a2b8c559-8a5b-4a4a-8205-9, Tilburg University, School of Economics and Management.
    2. repec:fth:tilbur:9998 is not listed on IDEAS
    3. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    4. Voorneveld, M. & Borm, P.E.M. & van Megen, F.J.C. & Tijs, S.H. & Facchini, G., 1999. "Congestion Games and Potentials Reconsidered," Other publications TiSEM 1d647323-c17d-41e9-a4d5-8, Tilburg University, School of Economics and Management.
    5. Thomas Quint & Martin Shubik, 1994. "A Model of Migration," Cowles Foundation Discussion Papers 1088, Cowles Foundation for Research in Economics, Yale University.
    6. Le Breton, M. & Weber, S., 1995. "Strong Equilibrium in a Model with Partial Rivalry," G.R.E.Q.A.M. 95a07, Universite Aix-Marseille III.
    7. 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.
    8. 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.
    9. Holzman, Ron & Law-Yone, Nissan, 1997. "Strong Equilibrium in Congestion Games," Games and Economic Behavior, Elsevier, vol. 21(1-2), pages 85-101, October.
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    Cited by:

    1. Fatima Khanchouche & Samir Sbabou & Hatem Smaoui & Abderrahmane Ziad, 2024. "Nash Equilibria in Two-Resource Congestion Games with Player-Specific Payoff Functions," Games, MDPI, vol. 15(2), pages 1-10, February.
    2. Fatima Khanchouche & Samir Sbabou & Hatem Smaoui & Abderrahmane Ziad, 2024. "Nash Equilibria in Two-Resource Congestion Games with Player-Specific Payoff Functions," Post-Print hal-04506452, HAL.
    3. Fatima Khanchouche & Samir Sbabou & Hatem Smaoui & Ziad Abderrahmane, 2023. "Congestion Games with Player-Specific Payoff Functions: The Case of Two Resources, Computation and Algorithms. First version," Economics Working Paper Archive (University of Rennes & University of Caen) 2023-08, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.

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    More about this item

    Keywords

    Singleton congestion games; Nash equilibria; ordinal preferences;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory

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