Maximum Nash welfare and other stories about EFX



Amanatidis, Georgios, Birmpas, Georgios, Filos-Ratsikas, Aris ORCID: 0000-0001-7868-8114, Hollender, Alexandros and Voudouris, Alexandros A
(2021) Maximum Nash welfare and other stories about EFX. Theoretical Computer Science, 863. pp. 69-85.

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Abstract

We consider the classic problem of fairly allocating indivisible goods among agents with additive valuation functions and explore the connection between two prominent fairness notions: maximum Nash welfare (MNW) and envy-freeness up to any good (EFX). We establish that an MNW allocation is always EFX as long as there are at most two possible values for the goods, whereas this implication is no longer true for three or more distinct values. As a notable consequence, this proves the existence of EFX allocations for these restricted valuation functions. While the efficient computation of an MNW allocation for two possible values remains an open problem, we present a novel algorithm for directly constructing EFX allocations in this setting. Finally, we study the question of whether an MNW allocation implies any EFX guarantee for general additive valuation functions under a natural new interpretation of approximate EFX allocations.

Item Type: Article
Uncontrolled Keywords: Fair division, Nash welfare, EFX, Approximation
Divisions: Faculty of Science and Engineering > School of Electrical Engineering, Electronics and Computer Science
Depositing User: Symplectic Admin
Date Deposited: 24 Jun 2021 10:01
Last Modified: 18 Jan 2023 21:37
DOI: 10.1016/j.tcs.2021.02.020
Related URLs:
URI: https://livrepository.liverpool.ac.uk/id/eprint/3127546