Note On the core of a collection of coalitions

Hans Reijnierse () and Jean Derks

International Journal of Game Theory, 1998, vol. 27, issue 3, 459 pages

Abstract: 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}.

Keywords: Core; ·; restricted; core; ·; non-degeneracy; ·; balancedness; ·; exactness (search for similar items in EconPapers)
Date: 1998-11-02
Note: Received May 1997/Final version May 1998
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