{"type":"ScholarlyArticle","title":"Improving Nash Social Welfare Approximations","authors":[{"name":"Jugal Garg","slug":"jugal-garg","given":"Jugal","family":"Garg","affiliation":"University of Illinois at Urbana-Champaign"},{"name":"Peter McGlaughlin","slug":"peter-mcglaughlin","given":"Peter","family":"McGlaughlin","affiliation":"University of Illinois at Urbana-Champaign"}],"abstract":"We consider the problem of fairly allocating a set of indivisible goods among n agents. Various fairness notions have been proposed within the rapidly growing field of fair division, but the Nash social welfare (NSW) serves as a focal point. In part, this follows from the 'unreasonable' fairness guarantees provided, in the sense that a max NSW allocation meets multiple other fairness metrics simultaneously, all while satisfying a standard economic concept of efficiency, Pareto optimality. However, existing approximation algorithms fail to satisfy all of the remarkable fairness guarantees offered by a max NSW allocation, instead targeting only the specific NSW objective. We address this issue by presenting a 2 max NSW, Prop-1, 1/(2n) MMS, and Pareto optimal allocation in strongly polynomial time. Our techniques are based on a market interpretation of a fractional max NSW allocation. We present novel definitions of fairness concepts in terms of market prices, and design a new scheme to round a market equilibrium into an integral allocation that provides most of the fairness properties of an integral max NSW allocation.","doi":"10.24963/ijcai.2019/42","url":"https://ijcai.org/proceedings/2019/42","pdf":"https://ijcai.org/proceedings/2019/0042.pdf","markdown":"https://ijcai.org/proceedings/2019/42.md","bibtex":"https://ijcai.org/proceedings/2019/bibtex/42","volume":{"slug":"2019","title":"Proceedings of the Twenty-Eighth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2019","url":"https://ijcai.org/proceedings/2019/","year":2019,"location":"Macao","dates":"10-16 August 2019","editors":"Sarit Kraus","isbn":"978-0-9992411-4-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2019"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":42,"pages":{"first":294,"last":300},"keywords":["Agent-based and Multi-agent Systems: Algorithmic Game Theory","Agent-based and Multi-agent Systems: Resource Allocation","Agent-based and Multi-agent Systems: Economic Paradigms, Auctions and Market-Based Systems"],"videos":[],"references":[{"position":1,"raw":"[Amanatidis et al., 2017] Georgios Amanatidis, Evangelos Markakis, Afshin Nikzad, and Amin Saberi. 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