The non-emptiness of the weak sequential core of a transferable utility game with uncertainty

Abstract

The weak sequential core of a transferable utility game with uncertainty (Habis and Herings, 2011) is considered. We give a necessary and sufficient condition for the non-emptiness of the weak sequential core. We show that a transferable utility game with uncertainty has a non-empty weak sequential core if and only if it is uniformly P-balanced on the cores.Furthermore, we introduce a subclass of transferable utility games with uncertainty, the class of generalized balanced games with universal veto control–which class properly includes the class of convex transferable utility games with uncertainty considered by (Habis and Herings, 2011)–and we show that every generalized balanced game with universal veto control has a non-empty weak sequential core.