{"type":"ScholarlyArticle","title":"Allocating Mixed Goods with Customized Fairness and Indivisibility Ratio","authors":[{"name":"Bo Li","slug":"bo-li","given":"Bo","family":"Li","affiliation":"The Hong Kong Polytechnic University"},{"name":"Zihao Li","slug":"zihao-li","given":"Zihao","family":"Li","affiliation":"Nanyang Technological University"},{"name":"Shengxin Liu","slug":"shengxin-liu","given":"Shengxin","family":"Liu","affiliation":"Harbin Institute of Technology , Shenzhen"},{"name":"Zekai Wu","slug":"zekai-wu","given":"Zekai","family":"Wu","affiliation":"Harbin Institute of Technology , Shenzhen"}],"abstract":"We consider the problem of fairly allocating a combination of divisible and indivisible goods. While fairness criteria like envy-freeness (EF) and proportionality (PROP) can always be achieved for divisible goods, only their relaxed versions, such as the “up to one” relaxations EF1 and PROP1, can be satisfied when the goods are indivisible. The “up to one” relaxations require the fairness conditions to be satisfied provided that one good can be completely eliminated or added in the comparison. In this work, we bridge the gap between the two extremes and propose “up to a fraction” relaxations for the allocation of mixed divisible and indivisible goods. The fraction is determined based on the proportion of indivisible goods, which we call the indivisibility ratio. The new concepts also introduce asymmetric conditions that are customized for individuals with varying indivisibility ratios. We provide both upper and lower bounds on the fractions of the modified item in order to satisfy the fairness criterion. Our results are tight up to a constant for EF and asymptotically tight for PROP.","doi":"10.24963/ijcai.2024/318","url":"https://ijcai.org/proceedings/2024/318","pdf":"https://ijcai.org/proceedings/2024/0318.pdf","markdown":"https://ijcai.org/proceedings/2024/318.md","bibtex":"https://ijcai.org/proceedings/2024/bibtex/318","volume":{"slug":"2024","title":"Proceedings of the Thirty-Third International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2024","url":"https://ijcai.org/proceedings/2024/","year":2024,"location":"Jeju, Korea","dates":"3-9 August 2024","editors":"Kate Larson","isbn":"978-1-956792-04-1","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2024"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":318,"pages":{"first":2868,"last":2876},"keywords":["Game Theory and Economic Paradigms: GTEP: Fair division"],"videos":[],"references":[{"position":1,"raw":"[Amanatidis et al., 2023] Georgios Amanatidis, Haris Aziz, Georgios Birmpas, Aris Filos-Ratsikas, Bo Li, Hervé Moulin, Alexandros A. 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