IDEAS home Printed from https://ideas.repec.org/a/spr/jogath/v27y1998i1p131-145.html
   My bibliography  Save this article

Values and potential of games with cooperation structure

Author

Listed:
  • Jesßs-Mario Bilbao

    (E. S. Ingenieros, University of Seville, Camino de los Descubrimientos, 41092 Sevilla, Spain)

Abstract

Games with cooperation structure are cooperative games with a family of feasible coalitions, that describes which coalitions can negotiate in the game. We study a model of cooperation structure and the corresponding restricted game, in which the feasible coalitions are those belonging to a partition system. First, we study a recursive procedure for computing the Hart and Mas-Colell potential of these games and we develop the relation between the dividends of Harsanyi in the restricted game and the worths in the original game. The properties of partition convex geometries are used to obtain formulas for the Shapley and Banzhaf values of the players in the restricted game $v^{ \cal L}$, in terms of the original game v. Finally, we consider the Owen multilinear extension for the restricted game.

Suggested Citation

  • Jesßs-Mario Bilbao, 1998. "Values and potential of games with cooperation structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 27(1), pages 131-145.
    • Handle: RePEc:spr:jogath:v:27:y:1998:i:1:p:131-145
    Note: Received April 1996/Revised version February 1997/Final version July 1997
    as

    Download full text from publisher

    File URL: http://link.springer.de/link/service/journals/00182/papers/8027001/80270131.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. Takao Asano & Hiroyuki Kojima, 2014. "Modularity and monotonicity of games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 80(1), pages 29-46, August.
    2. Algaba, A. & Bilbao, J.M. & Borm, P.E.M., 1999. "The Myerson Value for Union Stable Systems," Other publications TiSEM 022b6f46-8f76-4bb3-acab-3, Tilburg University, School of Economics and Management.
    3. René van den Brink & Gerard van der Laan & Valeri Vasil'ev, 0000. "The Restricted Core for Totally Positive Games with Ordered Players," Tinbergen Institute Discussion Papers 09-038/1, Tinbergen Institute.

    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:27:y:1998:i:1:p:131-145. 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.