IDEAS home Printed from https://ideas.repec.org/p/tut/cremwp/201115.html
   My bibliography  Save this paper

Nash equilibria in nonsymmetric singleton congestion games with exact partition

Author

Listed:
  • Abderrahmane ZIAD

    (University of Caen Basse-Normandie, CREM (UMR CNRS))

  • Samir SBABOU

    (University of Caen Basse-Normandie, CREM (UMR CNRS))

  • Hatem SMAOUI

    (CEMOI, Université de la Réunion)

Abstract

We define a new class of games, which we qualify as congestion games with exact partition. These games constitute a subfamily of singleton congestion games for which the players are restricted to choose only one strategy, but they each possess their own utility function. The aim of this paper is to develop a method leading to an easier identification of all Nash equilibria in this kind of congestion games. We also give a new proof establishing the existence of a Nash equilibrium in this type of games without invoking the potential function or the finite best-reply property.

Suggested Citation

  • Abderrahmane ZIAD & Samir SBABOU & Hatem SMAOUI, 2011. "Nash equilibria in nonsymmetric singleton congestion games with exact partition," Economics Working Paper Archive (University of Rennes & University of Caen) 201115, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.
    • Handle: RePEc:tut:cremwp:201115
    as

    Download full text from publisher

    File URL: https://ged.univ-rennes1.fr/nuxeo/site/esupversions/2df28a59-561c-47dd-865a-fc2d7222eedc
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. 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.
    2. Thomas Quint & Martin Shubik, 1994. "A Model of Migration," Cowles Foundation Discussion Papers 1088, Cowles Foundation for Research in Economics, Yale University.
    3. 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.
    4. repec:fth:tilbur:9998 is not listed on IDEAS
    5. Monderer, Dov & Shapley, Lloyd S., 1996. "Potential Games," Games and Economic Behavior, Elsevier, vol. 14(1), pages 124-143, May.
    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. Samir Sbabou & Hatem Smaoui & Abderrahmane Ziad, 2013. "A formula for Nash equilibria in monotone singleton congestion games," Economics Bulletin, AccessEcon, vol. 33(1), pages 334-339.
    2. Abderrahmane ZIAD & Samir SBABOU & Hatem SMAOUI, CEMOI, 2011. "Nonsymmetric singleton congestion games: case of two resources," Economics Working Paper Archive (University of Rennes & University of Caen) 201113, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.
    3. Olivier Tercieux & Mark Voorneveld, 2010. "The cutting power of preparation," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 71(1), pages 85-101, February.
    4. Roughgarden, Tim & Tardos, Eva, 2004. "Bounding the inefficiency of equilibria in nonatomic congestion games," Games and Economic Behavior, Elsevier, vol. 47(2), pages 389-403, May.
    5. Samir Sbabou & Hatem Smaoui & Abderrahmane Ziad, 2013. "Jeux de congestion finis à choix unique : Théorie, Equilibres, Applications -Calculs et Complexités-," Economics Working Paper Archive (University of Rennes & University of Caen) 201303, Center for Research in Economics and Management (CREM), University of Rennes, University of Caen and CNRS.
    6. Hideo Konishi, 2004. "Uniqueness of User Equilibrium in Transportation Networks with Heterogeneous Commuters," Transportation Science, INFORMS, vol. 38(3), pages 315-330, August.
    7. van Megen, F.J.C. & Facchini, G. & Borm, P.E.M. & Tijs, S.H., 1996. "Strong Nash Equilibria and the Potential Maimizer," Discussion Paper 1996-13, Tilburg University, Center for Economic Research.
    8. 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.
    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.
    10. Kukushkin, Nikolai S., 2018. "A universal construction generating potential games," Games and Economic Behavior, Elsevier, vol. 108(C), pages 331-340.
    11. repec:ebl:ecbull:v:3:y:2008:i:17:p:1-7 is not listed on IDEAS
    12. Lina Mallozzi, 2013. "An application of optimization theory to the study of equilibria for games: a survey," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 21(3), pages 523-539, September.
    13. Milchtaich, Igal, 2004. "Social optimality and cooperation in nonatomic congestion games," Journal of Economic Theory, Elsevier, vol. 114(1), pages 56-87, January.
    14. 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.
    15. Nikolai Kukushkin, 2007. "Congestion games revisited," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(1), pages 57-83, September.
    16. Sandholm, William H., 2001. "Potential Games with Continuous Player Sets," Journal of Economic Theory, Elsevier, vol. 97(1), pages 81-108, March.
    17. 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.
    18. H Peyton Young, 2014. "The Evolution of Social Norms," Economics Series Working Papers 726, University of Oxford, Department of Economics.
    19. Falk Armin & Kosfeld Michael, 2012. "It's all about Connections: Evidence on Network Formation," Review of Network Economics, De Gruyter, vol. 11(3), pages 1-36, September.
    20. Milchtaich, Igal & Winter, Eyal, 2002. "Stability and Segregation in Group Formation," Games and Economic Behavior, Elsevier, vol. 38(2), pages 318-346, February.
    21. Anthonisen, Niels, 1997. "On the Convergence of Beliefs within Populations in Games with Learning," Journal of Economic Theory, Elsevier, vol. 76(1), pages 169-184, September.

    More about this item

    Keywords

    Singleton congestion games; Nash equilibria; Potential function; Finite best-reply property.;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:tut:cremwp:201115. 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: GERMAIN Lucie (email available below). General contact details of provider: https://edirc.repec.org/data/crmrefr.html .

    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.