Cores of Partitioning Games
A generalization of assignment games, called partitioning games, is introduced. Given a ﬁnite set N of players, there is an a priori given subset pi of coalitions of N and only coalitions in pi play an essential role. Necessary and suﬀicient conditions for the non-emptiness of the cores of all games with essential coalitions pi are developed. These conditions appear extremely restrictive. However, when N is “large,” there are relatively few “types” of players, and members of pi are “small” and deﬁned in terms of numbers of players of each type contained in subsets, then approximate cores are non-empty.
Kaneko, Mamoru and Wooders, Myrna Holtz, "Cores of Partitioning Games" (1982). Cowles Foundation Discussion Papers. 856.