Monotonicity and the Aumann–Shapley cost-sharing method in the discrete case

• Cost-sharing in the discrete case.
• New characterization of the Aumann–Shapley cost-sharing method.
• Additivity is not employed.
• Monotonicity is employed.
• Only two basic axioms characterize the method.

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 perfectly divisible, for which Monderer and Neyman (1988) and Young (1985b) characterize the Aumann–Shapley price mechanism.