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EFX Exists for Three Agents

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arxiv 2002.05119 v3 pith:66IQLRIS submitted 2020-02-12 cs.GT

Bhaskar Ray Chaudhury , Jugal Garg , Kurt Mehlhorn This is my paper · ORCID
classification cs.GT
keywords agentsallocationthreeexistsitemsadditiveallocatedallocations
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abstract

We study the problem of distributing a set of indivisible items among agents with additive valuations in a $\mathit{fair}$ manner. The fairness notion under consideration is Envy-freeness up to any item (EFX). Despite significant efforts by many researchers for several years, the existence of EFX allocations has not been settled beyond the simple case of two agents. In this paper, we show constructively that an EFX allocation always exists for three agents. Furthermore, we falsify the conjecture by Caragiannis et al. by showing an instance with three agents for which there is a partial EFX allocation (some items are not allocated) with higher Nash welfare than that of any complete EFX allocation.

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Cited by 1 Pith paper

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Complete EFX Allocations Exist for Four Additive Agents and Up to Nine Goods

    cs.GT 2026-08 conditional novelty 7.0 of 10

    Every instance with four additive agents and up to nine indivisible goods admits a complete, zero-tolerant EFX allocation.

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