On Optimal Tradeoffs between EFX and Nash Welfare

Michal Feldman, Simon Mauras, Tomasz Ponitka

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

Abstract

A major problem in fair division is how to allocate a set of indivisible resources among agents fairly and efficiently. The goal of this work is to characterize the tradeoffs between two well-studied measures of fairness and efficiency - envy freeness up to any item (EFX) for fairness, and Nash welfare for efficiency - by saying, for given constants α and β, whether there exists an α-EFX allocation that guarantees a β-fraction of the maximum Nash welfare (β-MNW). For additive valuations, we show that for any α ∈ [0, 1], there exists a partial allocation that is α-EFX and α+11 -MNW. This tradeoff turns out to be tight (for every α) as demonstrated by an impossibility result that we give. We also show that for α ∈ [0, φ−1 ≈ 0.618] these partial allocations can be turned into complete allocations where all items are assigned. Furthermore, for any α ∈ [0, 1/2], we show that the tight tradeoff of α-EFX and α+11 -MNW with complete allocations holds for the more general setting of subadditive valuations. Our results improve upon the current state of the art, for both additive and subadditive valuations, and match the best-known approximations of EFX under complete allocations, regardless of Nash welfare guarantees. Notably, our constructions for additive valuations also provide EF1 and constant approximations for maximin share guarantees.

Original languageEnglish
Title of host publicationTechnical Tracks 14
EditorsMichael Wooldridge, Jennifer Dy, Sriraam Natarajan
Pages9688-9695
Number of pages8
Edition9
ISBN (Electronic)1577358872, 9781577358879
DOIs
StatePublished - 25 Mar 2024
Event38th AAAI Conference on Artificial Intelligence, AAAI 2024 - Vancouver, Canada
Duration: 20 Feb 202427 Feb 2024

Publication series

NameProceedings of the AAAI Conference on Artificial Intelligence
Number9
Volume38

Conference

Conference38th AAAI Conference on Artificial Intelligence, AAAI 2024
Country/TerritoryCanada
CityVancouver
Period20/02/2427/02/24

All Science Journal Classification (ASJC) codes

  • Artificial Intelligence

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