A Tight Negative Example for MMS Fair Allocations

Uriel Feige, Ariel Sapir, Laliv Tauber

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

Abstract

We consider the problem of allocating indivisible goods to agents with additive valuation functions. Kurokawa, Procaccia and Wang [JACM, 2018] present instances for which every allocation gives some agent less than her maximin share. We present such examples with larger gaps. For three agents and nine items, we design an instance in which at least one agent does not get more than a 3940 fraction of her maximin share. Moreover, we show that there is no negative example in which the difference between the number of items and the number of agents is smaller than six, and that the gap (of 140 ) of our example is worst possible among all instances with nine items. For n≥ 4 agents, we show examples in which at least one agent does not get more than a 1-1n4 fraction of her maximin share. In the instances designed by Kurokawa, Procaccia and Wang, the gap is exponentially small in n. Our proof techniques extend to allocation of chores (items of negative value), though the quantitative bounds for chores are different from those for goods. For three agents and nine chores, we design an instance in which the MMS gap is 143.

Original languageEnglish
Title of host publicationWeb and Internet Economics - 17th International Conference, WINE 2021, Proceedings
EditorsMichal Feldman, Hu Fu, Inbal Talgam-Cohen
PublisherSpringer Science and Business Media B.V.
Pages355-372
Number of pages18
ISBN (Electronic)978-3-030-94676-0
ISBN (Print)9783030946753
DOIs
StatePublished - 2022
Event17th International Conference on Web and Internet Economics, WINE 2021 - Virtual, Online
Duration: 14 Dec 202117 Dec 2021

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume13112 LNCS

Conference

Conference17th International Conference on Web and Internet Economics, WINE 2021
CityVirtual, Online
Period14/12/2117/12/21

All Science Journal Classification (ASJC) codes

  • Theoretical Computer Science
  • General Computer Science

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