Cost sharing solutions defined by non-negative eigenvectors

Abstract

The problem of sharing a cost M among n individuals, identified by some characteristic c i ∈ R + , appears in many real situations. Two important proposals on how to share the cost are the egalitarian and the proportional solutions. In different situations a combination of both distributions provides an interesting approach to the cost sharing problem. In this paper we obtain a family of (compromise) solutions associated to the Perron' eigenvectors of Levinger's transformations of a characteristics matrix A. This family includes both the egalitarian and proportional solutions, as well as a set of suitable intermediate proposals, which we analyze in some specific contexts, as claims problems and inventory cost games.

Resource allocations with guaranteed awards in claims problems

“…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. In fact, there are some solutions that always ensure a strictly positive quantity to each agent (with positive claim): this is the case of the constrained equal awards rule (Maimonides 2000), the α min solution (Giménez-Gómez and Peris 2014), or solutions that are defined by positive eigenvectors (Subiza et al 2015).…”