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...

When perfect recall is not satisfied, the informational contents of mixed and behavior strategies differ and are more than what the information partition describes. First, we consider two kinds of additional information strategies may carry, and show that such information leads to the perfect...