NTU-bankruptcy problems: consistency and the relative adjustment principle

This paper axiomatically studies bankruptcy problems with nontransferable utility by focusing on generalizations of consistency and the contested garment principle. On the one hand, we discuss several consistency notions and introduce the class of parametric bankruptcy rules which contains the proportional rule, the constrained relative equal awards rule, and the constrained relative equal losses rule. On the other hand, we introduce the class of adjusted bankruptcy rules and characterize the relative adjustment principle by truncation invariance, minimal rights first, and a weak form of relative symmetry.