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Note On the core of a collection of coalitions

  • Hans Reijnierse


    (Department of Mathematics, University of Nijmegen, Toernooiveld, 6525 ED Nijmegen, The Netherlands)

  • Jean Derks


    (Department of Mathematics, University of Maastricht, P.O.Box 616, 6200 MD Maastricht, The Netherlands)

For a collection of subsets of a finite set N we define its core to be equal to the polyhedral cone {x∈IRN: ∑i∈N xi=0 and ∑i∈Sxi\geq0 for all S∈}. This note describes several applications of this concept in the field of cooperative game theory. Especially collections are considered with core equal to {0}. This property of a one-point core is proved to be equivalent to the non-degeneracy and balancedness of . Further, the notion of exact cover is discussed and used in a second characterization of collections with core equal to {0}.

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Article provided by Springer in its journal International Journal of Game Theory.

Volume (Year): 27 (1998)
Issue (Month): 3 ()
Pages: 451-459

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Handle: RePEc:spr:jogath:v:27:y:1998:i:3:p:451-459
Note: Received May 1997/Final version May 1998
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