We consider Young (1985)s characterization of the Shapley value, and give a new proof of this axiomatization. Moreover, as applications of the new proof, we show that Young (1985)s axiomatization of the Shapley value works on various well-known subclasses of TU games.
When modeling game situations of incomplete information one usually considers the players hierarchies of beliefs, a source of all sorts of complications. Harsanyi (1967-68)s idea henceforth referred to as the Harsanyi program is that hierarchies of b
eliefs can be replaced by types. The types constitute the type space. In the purely measurable framework Heifetz and Samet (1998) formalize the concept of type spaces and prove the existence and the uniqueness of a universal type space. Meier (2001) shows that the purely measurable universal type space is complete, i.e., it is a consistent object. With the aim of adding the finishing touch to these results, we will prove in this paper that in the purely measurable framework every hierarchy of beliefs can be represented by a unique element of the complete universal type space.
