The Constrained Equal Awards Rule for Bankruptcy Problems with a Priori Unions

Abstract

In this paper, we provide two extensions of the constrained equal awards rule for bankruptcy situations to the class of bankruptcy situations with a priori unions. We present some characterisations and relations with corresponding games. The two new extensions are illustrated by a specific application.

Game-Theoretic Analysis of Bankruptcy and Taxation Problems: Recent Advances

“…For the random arrival rule, the main axiom is inspired by the consistency notion proposed by Hart and Mas-Colell [1989] for TU games that we mentioned earlier. These results are due to Borm et al [2005].…”

Axiomatic and game-theoretic analysis of bankruptcy and taxation problems: An update

“…A composite rule based on the proportional and constrained equal awards rules has also come out of axiomatic work. Papers on the subject are by González-Alcón, Borm, and Hendrickx (2003), Calleja, Borm, and Hendrickx (2005), Borm, Carpente, Casas-Méndez, Hendrickx (2005), Moreno-Ternero (2009), and Bergantiños, Lorenzo, and Lorenzo-Freire (2010a, 2010b. Ju, Miyagawa and Sakai (2007) and Hinojosa, Mármol, and Sánchez (2012), also offer results that pertain to this model.…”

“…Here too, consistency plays a key role. Borm, Carpente, Casas-Méndez, and Hendrickx (2005) enrich the base model by imagining that players are grouped in unions. They adapt the constrained equal awards rule to this context and give two characterizations of this extension.…”

Decentralized Rationing Problems

“…These authors define and characterize a two-stage extension of the adjusted proportional rule. In the same line, Borm et al (2005) define and characterize a two-stage extension of the constrained equal awards rule 2 within the framework of bankruptcy with a priori unions. Both studies are inspired in the classical paper by Owen (1977), who considers, for cooperative games, the a priori partition of the 1 We refer to these situations as either standard rationing problems in Chapter 2 or single-issue rationing problems in Chapter 3.…”

“…The latter use, in their characterization of the two-stage extension of the constrained equal awards rule, the axioms of equal treatment within the issues and equal treatment between the issues, 3 among other axioms. The first 3 Lorenzo-Freire et al (2010) also use these same axioms in their characterizations, but they call them equal treatment for the players within an issue and equal treatment for the of these properties states that if two agents have equal claims for an issue, they should receive equal amounts in this issue. The second states that if the total (aggregate) claim over two issues is the same, the total amount assigned to both issues should coincide.…”