IDEAS home Printed from https://ideas.repec.org/p/tin/wpaper/20130177.html
   My bibliography  Save this paper

Characterizing the Core via k-Core Covers

Author

Listed:
  • Estela Sánchez-Rodríguez

    (Vigo University, Spain)

  • Peter Borm

    (CentER, University of Tilburg, the Netherlands)

  • Arantza Estévez-Fernández

    (VU University Amsterdam)

  • M. Gloria Fiestras-Janeiro

    (Vigo University, Spain)

  • Manuel A. Mosquera

    (Vigo University, Spain)

Abstract

This paper extends the notion of individual minimal rights for a transferable utility game (TU-game) to coalitional minimal rights using minimal balanced families of a specific type, thus defining a corresponding minimal rights game. It is shown that the core of a TU-game coincides with the core of the corresponding minimal rights game. Moreover, the paper introduces the notion of the k-core cover as an extension of the core cover. The k-core cover of a TU-game consists of all efficient payoff vectors for which the total joint payoff for any coalition of size at most k is bounded from above by the value of this coalition in the corresponding dual game, and from below by the value of this coalition in the corresponding minimal rights game. It is shown that the core of a TU-game with player set N coincides with the ⌊|N |/2⌋-core cover. Furthermore, full characteriz ations of games for which a k-core cover is nonempty and for which a k-core cover coincides with the core are provided.

Suggested Citation

  • Estela Sánchez-Rodríguez & Peter Borm & Arantza Estévez-Fernández & M. Gloria Fiestras-Janeiro & Manuel A. Mosquera, 2013. "Characterizing the Core via k-Core Covers," Tinbergen Institute Discussion Papers 13-177/II, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20130177
    as

    Download full text from publisher

    File URL: https://papers.tinbergen.nl/13177.pdf
    Download Restriction: no
    ---><---

    More about this item

    Keywords

    Core; core cover; k-core cover; k-compromise admissibility; k-compromise stability; assignment games;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative 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:tin:wpaper:20130177. 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: Tinbergen Office +31 (0)10-4088900 (email available below). General contact details of provider: https://edirc.repec.org/data/tinbenl.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.