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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
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    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

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