Improving Nash social welfare approximations

Jugal Garg, Peter McGlaughlin

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We consider the problem of fairly allocating a set of indivisible goods among n agents. Various fairness notions have been proposed within the rapidly growing field of fair division, but the Nash social welfare (NSW) serves as a focal point. In part, this follows from the 'unreasonable' fairness guarantees provided, in the sense that a max NSW allocation meets multiple other fairness metrics simultaneously, all while satisfying a standard economic concept of efficiency, Pareto optimality. However, existing approximation algorithms fail to satisfy all of the remarkable fairness guarantees offered by a max NSW allocation, instead targeting only the specific NSW objective. We address this issue by presenting a 2 max NSW, Prop-1, 1/(2n) MMS, and Pareto optimal allocation in strongly polynomial time. Our techniques are based on a market interpretation of a fractional max NSW allocation. We present novel definitions of fairness concepts in terms of market prices, and design a new scheme to round a market equilibrium into an integral allocation in a way that provides most of the fairness properties of an integral max NSW allocation.

Original languageEnglish (US)
Title of host publicationProceedings of the 28th International Joint Conference on Artificial Intelligence, IJCAI 2019
EditorsSarit Kraus
PublisherInternational Joint Conferences on Artificial Intelligence
Number of pages7
ISBN (Electronic)9780999241141
StatePublished - 2019
Event28th International Joint Conference on Artificial Intelligence, IJCAI 2019 - Macao, China
Duration: Aug 10 2019Aug 16 2019

Publication series

NameIJCAI International Joint Conference on Artificial Intelligence
ISSN (Print)1045-0823


Conference28th International Joint Conference on Artificial Intelligence, IJCAI 2019

ASJC Scopus subject areas

  • Artificial Intelligence


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