{"type":"ScholarlyArticle","title":"Redividing the Cake","authors":[{"name":"Erel Segal-Halevi","slug":"erel-segal-halevi","given":"Erel","family":"Segal-Halevi","affiliation":"Ariel University , Ariel 40700 , Israel"}],"abstract":"A heterogeneous resource, such as a land-estate, is already divided among several agents in an unfair way.The challenge is to re-divide it among the agents in a way that balances fairness with ownership rights.We present re-division protocols that attain various combinations of fairness and ownership rights, in various settings differing in the geometric constraints on the allotments: (a) no geometric constraints; (b) connectivity --- the cake is a one-dimensional interval and each piece must be a contiguous interval; (c) rectangularity --- the cake is a two-dimensional rectangle and the pieces should be rectangles; (d) convexity --- the cake is a two-dimensional convex polygon and the pieces should be convex.","doi":"10.24963/ijcai.2018/69","url":"https://ijcai.org/proceedings/2018/69","pdf":"https://ijcai.org/proceedings/2018/0069.pdf","markdown":"https://ijcai.org/proceedings/2018/69.md","bibtex":"https://ijcai.org/proceedings/2018/bibtex/69","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":69,"pages":{"first":498,"last":504},"keywords":["Agent-based and Multi-agent Systems: Computational Social Choice","Agent-based and Multi-agent Systems: Resource Allocation","Knowledge Representation and Reasoning: Geometric, Spatial, and Temporal Reasoning"],"videos":[],"references":[{"position":1,"raw":"[Akopyan and Segal-Halevi, 2018] Arseniy Akopyan and Erel Segal-Halevi. 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