COWLES FOUNDATION FOR RESEARCH IN ECONOMICS
AT YALE UNIVERSITY

Box 208281
New Haven, CT 06520-8281

COWLES FOUNDATION DISCUSSION PAPER NO. 566

"A Necessary and Sufficient Condition for the Nonemptiness
of the Cores of Partitioning Games"

Mamoru Kaneko

November 1980

Let N be a finite set of players and let pi be a class of coalitions of N. We consider games with and without sidepayments such that only the coalitions in pi play essential roles but not the others. For an arbitrary pi, we get the class of all such games. The purpose of this note is to provide a necessary and sufficient condition with respect to pi for the nonemptiness of the cores of all games in the class.