For a collection Ω of subsets of a finite set N we define its core to be equal to the polyhedral cone {x ∈ IRN : Σi∈N xi = 0 and Σi∈S xi ≥ 0 for all S ∈ Ω}. This note describes several applications of this concept in the field of cooperative game theory. Especially collections Ω 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 Ω. Further, the notion of exact cover is discussed and used in a second characterization of collections Ω with core equal to {0}.
