{"type":"ScholarlyArticle","title":"Dynamic Fair Division Problem with General Valuations","authors":[{"name":"Bo Li","slug":"bo-li","given":"Bo","family":"Li","affiliation":"Stony Brook University"},{"name":"Wenyang Li","slug":"wenyang-li","given":"Wenyang","family":"Li","affiliation":"Melbourne University"},{"name":"Yingkai Li","slug":"yingkai-li","given":"Yingkai","family":"Li","affiliation":"Northwestern University"}],"abstract":"In this paper, we focus on how to dynamically allocate a divisible resource fairly among n players who arrive and depart over time. The players may have general heterogeneous valuations over the resource. It is known that the exact envy-free and proportional allocations may not exist in the dynamic setting [Walsh, 2011]. Thus, we will study to what extent we can guarantee the fairness in the dynamic setting. We first design two algorithms which are O(log n)-proportional and O(n)-envy-free for the setting with general valuations, and by constructing the adversary instances such that all dynamic algorithms must be at least Omega(1)-proportional and Omega(n/log n)-envy-free, we show that the bounds are tight up to a logarithmic factor. Moreover, we introduce the setting where the players' valuations are uniform on the resource but with different demands, which generalize the setting of [Friedman et al., 2015]. We prove an O(log n) upper bound and a tight lower bound for this case.","doi":"10.24963/ijcai.2018/52","url":"https://ijcai.org/proceedings/2018/52","pdf":"https://ijcai.org/proceedings/2018/0052.pdf","markdown":"https://ijcai.org/proceedings/2018/52.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/52","volume":{"slug":"2018","title":"Proceedings of the Twenty-Seventh International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2018","url":"https://ijcai.org/proceedings/2018/","year":2018,"location":"Stockholm","dates":"13-19 July 2018","editors":"Jérôme Lang","isbn":"978-0-9992411-2-7","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2018"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":52,"pages":{"first":375,"last":381},"keywords":["Agent-based and Multi-agent Systems: Algorithmic Game Theory","Agent-based and Multi-agent Systems: Resource Allocation"],"videos":[],"references":[{"position":1,"raw":"[Alon, 1987] Noga Alon. 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