A new approach for bounding awards in bankruptcy problems

Abstract

The solution for the 'Contested Garment Problem', proposed in the Babylonic Talmud, suggests that each agent should receive at least some part of the resources whenever the claim overcomes the available amount. In this context, we propose a new method to define lower bounds on awards, an idea that has underlied the theoretical analysis of claims problems from its beginning (O'Neill, 1982) to present day (Dominguez and Thomson, 2006). Specifically, starting from the fact that a society establishes its own set of commonly accepted principles, our proposal ensures to each agent the smallest amount she gets according to all the admissible rules. As in general this new bound will not exhaust the endowment, we analyze its recursive application for different sets of principles.

Resource allocations with guaranteed awards in claims problems

“…From a theoretical point of view, the idea of establishing minimum guarantees on awards underlies the analysis of claims problems from its beginning (O'Neill 1982) up to the present day (Giménez-Gómez and Marco-Gil 2014). Indeed, for each problem, the formal definition of a rule already includes the requirement that awards be nonnegative, which represents a lower bound on awards.…”

“…Afterwards, the recursive application of a lower bound has been analyzed in the literature, showing that (under some mild conditions) this process provides a unique rule. In particular, Dominguez (2013) and Giménez-Gómez and Marco-Gil (2014), among others, find out that some well known rules are retrieved by recursively applying lower bounds and, consequently, they provide new axiomatic characterizations of classical rules.…”

On the Difficulty of Budget Allocation in Claims Problems with Indivisible Items and Prices

“…In the context of claims problems with indivisibilities, several papers have proposed different type of solutions. Moulin ( 2000 ), Herrero and Martínez ( 2008a ), Chen ( 2015 ) use priority methods, while Giménez-Gómez and Vilella Bach ( 2012 ) adopt a P-rights recursive process, described in Giménez-Gómez and Marco-Gil ( 2014 ), to ensure weak order preservation. 5 Discrete claim models have been widely used to deal with scarce resources in technological problems such as mobile radio networks (Lucas-Estañ et al.…”