Note On the core of a collection of coalitions

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}.