TY - JOUR

T1 - Efficient Fair Division with Minimal Sharing

AU - Sandomirskiy, Fedor

AU - Segal-Halevi, Erel

N1 - Publisher Copyright:
Copyright: © 2022 INFORMS

PY - 2022/5/1

Y1 - 2022/5/1

N2 - A collection of objects, some of which are good and some of which are bad, is to be divided fairly among agents with different tastes, modeled by additive utility functions. If the objects cannot be shared, so that each of them must be entirely allocated to a single agent, then a fair division may not exist. What is the smallest number of objects that must be shared between two or more agents to attain a fair and efficient division? In this paper, fairness is understood as proportionality or envy-freeness and efficiency as fractional Pareto-optimality. We show that, for a generic instance of the problem (all instances except a zero-measure set of degenerate problems), a fair fractionally Pareto-optimal division with the smallest possible number of shared objects can be found in polynomial time, assuming that the number of agents is fixed. The problem becomes computationally hard for degenerate instances, where agents' valuations are aligned for many objects.

AB - A collection of objects, some of which are good and some of which are bad, is to be divided fairly among agents with different tastes, modeled by additive utility functions. If the objects cannot be shared, so that each of them must be entirely allocated to a single agent, then a fair division may not exist. What is the smallest number of objects that must be shared between two or more agents to attain a fair and efficient division? In this paper, fairness is understood as proportionality or envy-freeness and efficiency as fractional Pareto-optimality. We show that, for a generic instance of the problem (all instances except a zero-measure set of degenerate problems), a fair fractionally Pareto-optimal division with the smallest possible number of shared objects can be found in polynomial time, assuming that the number of agents is fixed. The problem becomes computationally hard for degenerate instances, where agents' valuations are aligned for many objects.

KW - discrete objects

KW - envy-freeness

KW - fair division

KW - fractional Pareto-optimality

KW - polynomial-time algorithm

KW - proportional fairness

UR - http://www.scopus.com/inward/record.url?scp=85134882025&partnerID=8YFLogxK

U2 - 10.1287/OPRE.2022.2279

DO - 10.1287/OPRE.2022.2279

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AN - SCOPUS:85134882025

SN - 0030-364X

VL - 70

SP - 1762

EP - 1782

JO - Operations Research

JF - Operations Research

IS - 3

ER -