Characterizing the Core via K-Core Covers

S.M. Sanchez, P.E.M. Borm, A. Estevez

Research output: Working paperDiscussion paperOther research output

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 ? 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.
Original languageEnglish
Place of PublicationAmsterdam
PublisherTinbergen Institute
Number of pages26
Volume2013-177/II
Publication statusPublished - 1 Dec 2013

Keywords

  • Core
  • core cover
  • k-compromise admissibility
  • k-compromise stability
  • assignment games

Cite this

Sanchez, S. M., Borm, P. E. M., & Estevez, A. (2013). Characterizing the Core via K-Core Covers. Amsterdam: Tinbergen Institute.
Sanchez, S.M. ; Borm, P.E.M. ; Estevez, A. / Characterizing the Core via K-Core Covers. Amsterdam : Tinbergen Institute, 2013.
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Sanchez, SM, Borm, PEM & Estevez, A 2013 'Characterizing the Core via K-Core Covers' Tinbergen Institute, Amsterdam.

Characterizing the Core via K-Core Covers. / Sanchez, S.M.; Borm, P.E.M.; Estevez, A.

Amsterdam : Tinbergen Institute, 2013.

Research output: Working paperDiscussion paperOther research output

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AU - Estevez, A.

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N2 - 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 ? 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.

AB - 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 ? 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.

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KW - k-compromise stability

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Sanchez SM, Borm PEM, Estevez A. Characterizing the Core via K-Core Covers. Amsterdam: Tinbergen Institute. 2013 Dec 1.