Fair Allocation Without Trade

TL;DR

This paper develops algorithms for fair item allocation among agents, extending fairness notions to broader utility models and providing polynomial-time solutions for two key fairness criteria.

Contribution

It formalizes two fairness notions in economic terms, extends them to general utilities, and offers polynomial-time algorithms for fair allocations under both notions.

Findings

Polynomial-time algorithm for Ghodsi et al.'s fairness notion

Market equilibrium approach for Dolev et al.'s fairness notion

Extension of fairness notions to broader utility classes

Abstract

We consider the age-old problem of allocating items among different agents in a way that is efficient and fair. Two papers, by Dolev et al. and Ghodsi et al., have recently studied this problem in the context of computer systems. Both papers had similar models for agent preferences, but advocated different notions of fairness. We formalize both fairness notions in economic terms, extending them to apply to a larger family of utilities. Noting that in settings with such utilities efficiency is easily achieved in multiple ways, we study notions of fairness as criteria for choosing between different efficient allocations. Our technical results are algorithms for finding fair allocations corresponding to two fairness notions: Regarding the notion suggested by Ghodsi et al., we present a polynomial-time algorithm that computes an allocation for a general class of fairness notions, in which their notion is included. For the other, suggested by Dolev et al., we show that a competitive market equilibrium achieves the desired notion of fairness, thereby obtaining a polynomial-time algorithm that computes such a fair allocation and solving the main open problem raised by Dolev et al.