IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v28y1999i2p229-240.html
   My bibliography  Save this article

On the bargaining set, kernel and core of superadditive games

Author

Listed:
  • TamÂs Solymosi

    (Department of Operations Research, Budapest University of Economic Sciences, 1828 Budapest, Pf. 489, Hungary)

Abstract

We prove that for superadditive games a necessary and sufficient condition for the bargaining set to coincide with the core is that the monotonic cover of the excess game induced by a payoff be balanced for each imputation in the bargaining set. We present some new results obtained by verifying this condition for specific classes of games. For N-zero-monotonic games we show that the same condition required at each kernel element is also necessary and sufficient for the kernel to be contained in the core. We also give examples showing that to maintain these characterizations, the respective assumptions on the games cannot be lifted.

Suggested Citation

  • TamÂs Solymosi, 1999. "On the bargaining set, kernel and core of superadditive games," International Journal of Game Theory, Springer;Game Theory Society, vol. 28(2), pages 229-240.
    • Handle: RePEc:spr:jogath:v:28:y:1999:i:2:p:229-240
    Note: Received: March 1998/Revised version: December 1998
    as

    Download full text from publisher

    File URL: http://link.springer.de/link/service/journals/00182/papers/9028002/90280229.pdf
    Download Restriction: Access to the full text of the articles in this series is restricted
    ---><---

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

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Peter Sudhölter & Jos A. M. Potters, 2001. "The semireactive bargaining set of a cooperative game," International Journal of Game Theory, Springer;Game Theory Society, vol. 30(1), pages 117-139.
    2. Atay, Ata & Solymosi, Tamás, 2018. "On bargaining sets of supplier-firm-buyer games," Economics Letters, Elsevier, vol. 167(C), pages 99-103.
    3. Hendrickx, R.L.P. & Borm, P.E.M. & Timmer, J.B., 2000. "On Convexity for NTU-Games," Other publications TiSEM ef12f1e8-87f5-41b4-97e4-7, Tilburg University, School of Economics and Management.
    4. Michel Le Breton & Karine Van Der Straeten, 2017. "Alliances Électorales et Gouvernementales : La Contribution de la Théorie des Jeux Coopératifs à la Science Politique," Revue d'économie politique, Dalloz, vol. 127(4), pages 637-736.
    5. Ata Atay & Eric Bahel & Tamás Solymosi, 2023. "Matching markets with middlemen under transferable utility," Annals of Operations Research, Springer, vol. 322(2), pages 539-563, March.
    6. Bezalel Peleg & Peter Sudhölter, 2015. "On Bargaining Sets of Convex NTU Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 17(04), pages 1-7.
    7. Marina Nunez Oliva & Carlos Rafels Pallarola, 2001. "The extreme core allocations of the assignment game," Working Papers in Economics 65, Universitat de Barcelona. Espai de Recerca en Economia.
    8. Massimiliano Amarante & Luigi Montrucchio, 2010. "The bargaining set of a large game," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 43(3), pages 313-349, June.
    9. Jesús Getán & Josep Izquierdo & Jesús Montes & Carles Rafels, 2015. "The bargaining set for almost-convex games," Annals of Operations Research, Springer, vol. 225(1), pages 83-89, February.
    10. Josep Maria Izquierdo Aznar & Carlos Rafels Pallarola, 2002. "Coalitionally Monotonic Set-solutions for Cooperative TU Games," Working Papers in Economics 75, Universitat de Barcelona. Espai de Recerca en Economia.
    11. Bahel, Eric, 2021. "Hyperadditive games and applications to networks or matching problems," Journal of Economic Theory, Elsevier, vol. 191(C).
    12. Grahn, Sofia, 2001. "Core and Bargaining Set of Shortest Path Games," Working Paper Series 2001:3, Uppsala University, Department of Economics.
    13. Massimiliano Amarante & Luigi Montrucchio, 2007. "Mas-Colell Bargaining Set of Large Games," Carlo Alberto Notebooks 63, Collegio Carlo Alberto.
    14. Josep M. Izquierdo & Carles Rafels, 2010. "On the coincidence between the Shimomuras bargaining sets and the core," Working Papers in Economics 241, Universitat de Barcelona. Espai de Recerca en Economia.
    15. Ruud Hendrickx & Judith Timmer & Peter Borm, 2002. "A note on NTU convexity," International Journal of Game Theory, Springer;Game Theory Society, vol. 31(1), pages 29-37.
    16. Tamás Solymosi, 2008. "Bargaining sets and the core in partitioning games," 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. 16(4), pages 425-440, December.
    17. Hendrickx, R.L.P., 2004. "Cooperation and allocation," Other publications TiSEM ab33e762-204c-46e2-86b1-0, Tilburg University, School of Economics and Management.
    18. Arnold Polanski, 2016. "Matching structure and bargaining outcomes in buyer–seller networks," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(4), pages 767-776, April.
    19. Josep M Izquierdo & Carles Rafels, 2012. "On the coincidence of the core and the bargaining sets," Economics Bulletin, AccessEcon, vol. 32(3), pages 2035-2043.
    20. Drechsel, J. & Kimms, A., 2010. "Computing core allocations in cooperative games with an application to cooperative procurement," International Journal of Production Economics, Elsevier, vol. 128(1), pages 310-321, November.
    21. Daniel Granot, 2010. "The reactive bargaining set for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 39(1), pages 163-170, March.
    22. Saadia El Obadi & Silvia Miquel, 2019. "Assignment Games with a Central Player," Group Decision and Negotiation, Springer, vol. 28(6), pages 1129-1148, December.

    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:28:y:1999:i:2:p:229-240. 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.

    We have no bibliographic references for this item. You can help adding them by using 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.