The proportional partitional Shapley value

Abstract

A new coalitional value is proposed under the hypothesis of isolated unions. The main difference between this value and the Aumann–Drèze value is that the allocations within each union are not given by the Shapley value of the restricted game but proportionally to the Shapley value of the original game. Axiomatic characterizations of the new value, examples illustrating its application and a comparative discussion are provided.