{"type":"ScholarlyArticle","title":"Maximum Nash Welfare and Other Stories About EFX","authors":[{"name":"Georgios Amanatidis","slug":"georgios-amanatidis","given":"Georgios","family":"Amanatidis","affiliation":"University of Essex; University of Amsterdam; Sapienza University of Rome"},{"name":"Georgios Birmpas","slug":"georgios-birmpas","given":"Georgios","family":"Birmpas","affiliation":"University of Oxford"},{"name":"Aris Filos-Ratsikas","slug":"aris-filos-ratsikas","given":"Aris","family":"Filos-Ratsikas","affiliation":"University of Liverpool"},{"name":"Alexandros Hollender","slug":"alexandros-hollender","given":"Alexandros","family":"Hollender","affiliation":"University of Oxford"},{"name":"Alexandros A. Voudouris","slug":"alexandros-a-voudouris","given":"Alexandros A.","family":"Voudouris","affiliation":"University of Essex; University of Oxford"}],"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.","doi":"10.24963/ijcai.2020/4","url":"https://ijcai.org/proceedings/2020/4","pdf":"https://ijcai.org/proceedings/2020/0004.pdf","markdown":"https://ijcai.org/proceedings/2020/4.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/4","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":4,"pages":{"first":24,"last":30},"keywords":["Agent-based and Multi-agent Systems: Economic Paradigms, Auctions and Market-Based Systems","Agent-based and Multi-agent Systems: Computational Social Choice"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/24131/file_24131.m3u8","length_sec":260,"provider":"hls"}],"references":[{"position":1,"raw":"[Aleksandrov and Walsh, 2019] M. 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