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$$k$$ k -core covers and the core

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  • E. Sánchez-Rodríguez
  • P. Borm
  • A. Estévez-Fernández
  • M. Fiestras-Janeiro
  • M. Mosquera

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 $$k$$ k -core cover as an extension of the core cover. The $$k$$ 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 $$k$$ 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 $$N$$ N coincides with the largest integer below or equal to $$\frac{|N|}{2}$$ | N | 2 -core cover. Furthermore, full characterizations of games for which a $$k$$ k -core cover is nonempty and for which a $$k$$ k -core cover coincides with the core are provided. Copyright Springer-Verlag Berlin Heidelberg 2015

Suggested Citation

  • E. Sánchez-Rodríguez & P. Borm & A. Estévez-Fernández & M. Fiestras-Janeiro & M. Mosquera, 2015. "$$k$$ k -core covers and the core," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 81(2), pages 147-167, April.
    • Handle: RePEc:spr:mathme:v:81:y:2015:i:2:p:147-167
    DOI: 10.1007/s00186-014-0490-9
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    References listed on IDEAS

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    Cited by:

    1. A. Estévez-Fernández & P. Borm & M. G. Fiestras-Janeiro & M. A. Mosquera & E. Sánchez-Rodríguez, 2017. "On the 1-nucleolus," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 86(2), pages 309-329, October.
      • Estévez-Fernández , M.A. & Borm, Peter & Fiestras, & Mosquera, & Sanchez,, 2017. "On the 1-nucleolus," Other publications TiSEM a8ce6687-c87a-4131-98f7-3, Tilburg University, School of Economics and Management.

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