EFX Exists for Three Agents-Reference-Cited by-同舟云学术

EFX Exists for Three Agents

Published:2023-09-04 Issue: Volume: Page:
ISSN:0004-5411
Container-title:Journal of the ACM
language:en
Short-container-title:J. ACM

Author:

Chaudhury Bhaskar Ray¹,Garg Jugal¹,Mehlhorn Kurt²

Affiliation:

1. University of Illinois at Urbana-Champaign, USA

2. Max Planck Institute for Informatics, Saarland Informatics Campus, Germany

Abstract

We study the problem of distributing a set of indivisible goods among agents with additive valuations in a fair manner. The fairness notion under consideration is envy-freeness up to any good (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 of Caragiannis et al. [9] by showing an instance with three agents for which there is a partial EFX allocation (some goods are not allocated) with higher Nash welfare than that of any complete EFX allocation.

Publisher

Association for Computing Machinery (ACM)

Subject

Artificial Intelligence,Hardware and Architecture,Information Systems,Control and Systems Engineering,Software

Link

https://dl.acm.org/doi/pdf/10.1145/3616009

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