Lower bounds and resource allocation

Abstract

The existence of lower bounds that guarantee a minimum to each agent involved in an allocation (claims) problem has been widely analysed in the literature. When focusing in claims problems, four lower bounds in what any individual should receive are the minimal right (Curiel et al., 1987), the fair lower bound (Moulin, 2002), securement (Moreno-Ternero and Villar, 2004) and the min lower bound Dominguez (2013). In the current paper we impose that a mechanism should fulfill one of the mentioned lower bound (we call this property respect of the lower bound, RB) and compare the mechanisms obtained by using RB together with some additional properties. We provide new characterizations of the so-called uniform rules (constrained equal awards, constrained equal losses) and the Ibn Ezra’s proposal.