{"type":"ScholarlyArticle","title":"Fair Division of Time: Multi-layered Cake Cutting","authors":[{"name":"Hadi Hosseini","slug":"hadi-hosseini","given":"Hadi","family":"Hosseini","affiliation":"Rochester Institute of Technology , USA"},{"name":"Ayumi Igarashi","slug":"ayumi-igarashi","given":"Ayumi","family":"Igarashi","affiliation":"National Institute of Informatics , Japan"},{"name":"Andrew Searns","slug":"andrew-searns","given":"Andrew","family":"Searns","affiliation":"Rochester Institute of Technology , USA"}],"abstract":"We initiate the study of multi-layered cake cutting with the goal of fairly allocating multiple divisible resources (layers of a cake) among a set of agents. The key requirement is that each agent can only utilize a single resource at each time interval. Several real-life applications exhibit such restrictions on overlapping pieces, for example, assigning time intervals over multiple facilities and resources or assigning shifts to medical professionals. We investigate the existence and computation of envy-free and proportional allocations. We show that envy-free allocations that are both feasible and contiguous are guaranteed to exist for up to three agents with two types of preferences, when the number of layers is two. We further devise an algorithm for computing proportional allocations for any number of agents when the number of layers is factorable to three and/or some power of two.","doi":"10.24963/ijcai.2020/26","url":"https://ijcai.org/proceedings/2020/26","pdf":"https://ijcai.org/proceedings/2020/0026.pdf","markdown":"https://ijcai.org/proceedings/2020/26.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/26","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":26,"pages":{"first":182,"last":188},"keywords":["Agent-based and Multi-agent Systems: Algorithmic Game Theory","Agent-based and Multi-agent Systems: Computational Social Choice"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/25239/file_25239.m3u8","length_sec":281,"provider":"hls"}],"references":[{"position":1,"raw":"[Aziz and Mackenzie, 2016a] Haris Aziz and Simon Macken- zie. 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