Proportionality, Equality, and Duality in Bankruptcy Problems with Nontransferable Utility

Abstract

This paper analyzes bankruptcy problems with nontransferable utility as a generalization of bankruptcy problems with monetary estate and claims. Following the classical axiomatic theory of bankruptcy, we formulate some appropriate properties for NTU-bankruptcy rules and study their implications. We explore duality of bankruptcy rules and we derive several characterizations of the generalized proportional rule and the constrained relative equal awards rule.

NTU-bankruptcy problems: consistency and the relative adjustment principle

“…A bankruptcy problem with nontransferable utility (cf. Dietzenbacher et al (2016)) is a triple (N, E, c) in which E ⊆ R N + is a nonempty, closed, bounded, comprehensive, and nonleveled estate, and c ∈ WUC(E) is a vector of claims. Let BR N denote the class of all bankruptcy problems with claimant set N .…”

“…The proportional rule Prop on BR N (cf. Dietzenbacher et al (2016)) assigns to any (E, c) ∈ BR N the payoff allocation…”

“…Orshan, Valenciano, and Zarzuelo (2003), Estévez-Fernández, Borm, and Fiestras-Janeiro (2014), and Dietzenbacher (2017) studied NTU-bankruptcy problems from a game theoretic perspective by defining an appropriate coalitional bankruptcy game and focusing on the structure of the core. Instead, we continue on the axiomatic approach of Dietzenbacher, Estévez-Fernández, Borm, and Hendrickx (2016) by formulating some appropriate properties for bankruptcy rules and studying their implications.…”

“…1 Dietzenbacher et al (2016) explored proportionality, equality, and duality in the context of NTU-bankruptcy problems and introduced the proportional rule, the constrained relative equal awards rule, and the constrained relative equal losses rule. They extended axiomatic characterizations by adequately generalizing the corresponding properties for TU-bankruptcy rules to NTU-bankruptcy rules.…”

“…This paper is organized in the following way. In Section 2, we provide an overview of NTU-bankruptcy theory based on Dietzenbacher et al (2016). Section 3 discusses several consistency notions and introduces the class of parametric bankruptcy rules.…”