We consider games with n players and r alternatives. In these games each player must choose one and only one alternative, reaching an ordered partition of the set of players. An extension of the Shapley value to this framework is studied.

We give an axiomatization of the Aumann–Shapley cost-sharing method in the discrete case by means of monotonicity and no merging or splitting (Sprumont, 2005). Monotonicity has not yet been employed to characterize this method in such a case, by contrast with the case in which goods are...