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...

According to Maschler, Peleg and Shapley (1972) the bargaining set of a convex game coincides with its core and the kernel consists of the nucleolus only. In this paper we prove the same properties for [Gamma]-component additive games (= graph restricted games in the sense of Owen (1986)) if...