Additive rules in discrete allocation problems

In this paper, we study allocation problems and other related problems where a discrete estate should be divided among agents who have claims on it. We characterize the set of rules satisfying additivity on the estate along with additivity on the estate and the claims. These results complete the characterizations given by Bergantiños and Vidal-Puga (Mathematical Social Sciences 47 (2004), 87–101) in the continuous case.