{"type":"ScholarlyArticle","title":"Networked Fairness in Cake Cutting","authors":[{"name":"Xiaohui Bei","slug":"xiaohui-bei","given":"Xiaohui","family":"Bei","affiliation":"School of Physical and Mathematical Sciences , Nanyang Technological University"},{"name":"Youming Qiao","slug":"youming-qiao","given":"Youming","family":"Qiao","affiliation":"Centre for Quantum Software and Information , University of Technology Sydney"},{"name":"Shengyu Zhang","slug":"shengyu-zhang","given":"Shengyu","family":"Zhang","affiliation":"Department of Computer Science and Engineering , The Chinese University of Hong Kong"}],"abstract":"We introduce a graphical framework for fair division in cake cutting, where comparisons between agents are limited by an underlying network structure. We generalize the classical fairness notions of envy-freeness and proportionality in this graphical setting. An allocation is called envy-free on a graph if no agent envies any of her neighbor's share, and is called proportional on a graph if every agent values her own share no less than the average among her neighbors, with respect to her own measure. These generalizations enable new research directions in developing simple and efficient algorithms that can produce fair allocations under specific graph structures.\r\n\r\nOn the algorithmic frontier, we first propose a moving-knife algorithm that outputs an envy-free allocation on trees. The algorithm is significantly simpler than the discrete and bounded envy-free algorithm introduced in [Aziz and Mackenzie, 2016] for compete graphs. Next, we give a discrete and bounded algorithm for computing a proportional allocation on transitive closure of trees, a class of graphs by taking a rooted tree and connecting all its ancestor-descendant pairs.","doi":"10.24963/ijcai.2017/508","url":"https://ijcai.org/proceedings/2017/508","pdf":"https://ijcai.org/proceedings/2017/0508.pdf","markdown":"https://ijcai.org/proceedings/2017/508.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/508","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Multidisciplinary Topics and Applications","track":"Main track","number":508,"pages":{"first":3632,"last":3638},"keywords":["Knowledge Representation, Reasoning, and Logic: Game Theory","Agent-based and Multi-agent Systems: Coordination and cooperation","Multidisciplinary Topics and Applications: AI and Social Sciences","Agent-based and Multi-agent Systems: Social Choice Theory"],"videos":[],"references":[{"position":1,"raw":"[Abebe et al., 2016] Rediet Abebe, Jon Kleinberg, and David Parkes. 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