On the linearity property for allocation problems and bankruptcy problems

Abstract

This work provides an analysis of linear rules for bankruptcy problems and allocation problems from an axiomatic point of view and we extend the study of the additivity property presented in Bergantiños and Méndez-Naya [1] and Bergantiños and Vidal-Puga [2]. We offer a decomposition for the space of allocation problems into direct sum of subspaces that are relevant to the study of linear rules and obtain characterizations of certain classes of rules. Furthermore, for bankruptcy problems we propose an alternative version of the additivity property.