k -core covers and the core

E. Sanchez-Rodriguez, P. Borm, M.A. Estevez Fernandez, M.G. Fiestras-Janeiro, M.A. Mosquera

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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.
Original languageEnglish
Pages (from-to)147-167
Number of pages21
JournalMathematical Methods of Operations Research
Volume81
Issue number2
Early online date1 Jan 2015
DOIs
Publication statusPublished - 2015

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Bibliographical note

April 2015, Volume 81, Issue 2, pp 147-167

Cite this

Sanchez-Rodriguez, E., Borm, P., Estevez Fernandez, M. A., Fiestras-Janeiro, M. G., & Mosquera, M. A. (2015). k -core covers and the core. Mathematical Methods of Operations Research, 81(2), 147-167. https://doi.org/10.1007/s00186-014-0490-9