We prove the nonemptiness of the core of a continuum game without side payments where only small coalitions--ones bounded in absolute size of finite cardinality--are permitted. This result covers assignment games with a continuum of players and includes combinations of several assignment 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...