This paper explores additivity-like properties ful led by bankruptcy rules. Our main result is that the unique rule satisfying an adittivity-like property is the Minimal Overlap proposed by O'Neill. We also propose some conections relative to additivity properties in close frameworks as bargaining rules.This work is partially supported by the Institut Valencià d´Investigacions Econòmiques and the Spanish Ministerio de Educación y Ciencia under projects SEJ2007-62656 (Alcalde) and SEJ2007-64649 (Marco-Gil and Silva). Marco-Gil also acknowledges support by the Fundación Séneca of the Agencia de Ciencia y Tecnología of the Murcian Region, under project 05838/PHCS/07 (Programa de Generación Cientìfico de Excelencia)
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