License: Creative Commons Attribution 4.0 International license (CC BY 4.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ESA.2021.66
URN: urn:nbn:de:0030-drops-146478
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2021/14647/
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Mahara, Ryoga

Extension of Additive Valuations to General Valuations on the Existence of EFX

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LIPIcs-ESA-2021-66.pdf (0.7 MB)

Abstract

Envy-freeness is one of the most widely studied notions in fair division. Since envy-free allocations do not always exist when items are indivisible, several relaxations have been considered. Among them, possibly the most compelling concept is envy-freeness up to any item (EFX). We study the existence of EFX allocations for general valuations. The existence of EFX allocations is a major open problem. For general valuations, it is known that an EFX allocation always exists (i) when n = 2 or (ii) when all agents have identical valuations, where n is the number of agents. it is also known that an EFX allocation always exists when one can leave at most n-1 items unallocated.
We develop new techniques and extend some results of additive valuations to general valuations on the existence of EFX allocations. We show that an EFX allocation always exists (i) when all agents have one of two general valuations or (ii) when the number of items is at most n+3. We also show that an EFX allocation always exists when one can leave at most n-2 items unallocated. In addition to the positive results, we construct an instance with n = 3 in which an existing approach does not work as it is.

BibTeX - Entry

@InProceedings{mahara:LIPIcs.ESA.2021.66,
  author =	{Mahara, Ryoga},
  title =	{{Extension of Additive Valuations to General Valuations on the Existence of EFX}},
  booktitle =	{29th Annual European Symposium on Algorithms (ESA 2021)},
  pages =	{66:1--66:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-204-4},
  ISSN =	{1868-8969},
  year =	{2021},
  volume =	{204},
  editor =	{Mutzel, Petra and Pagh, Rasmus and Herman, Grzegorz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/opus/volltexte/2021/14647},
  URN =		{urn:nbn:de:0030-drops-146478},
  doi =		{10.4230/LIPIcs.ESA.2021.66},
  annote =	{Keywords: Discrete Fair Division, EFX allocations, General Valuations}
}

Keywords: Discrete Fair Division, EFX allocations, General Valuations
Collection: 29th Annual European Symposium on Algorithms (ESA 2021)
Issue Date: 2021
Date of publication: 31.08.2021

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