{"type":"ScholarlyArticle","title":"Truthful Fair Mechanisms for Allocating Mixed Divisible and Indivisible Goods","authors":[{"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":"Xinhang Lu","slug":"xinhang-lu","given":"Xinhang","family":"Lu","affiliation":"UNSW Sydney"},{"name":"Biaoshuai Tao","slug":"biaoshuai-tao","given":"Biaoshuai","family":"Tao","affiliation":"Shanghai Jiao Tong University"}],"abstract":"We study the problem of designing truthful and fair mechanisms when allocating a mixture of divisible and indivisible goods. We first show that there does not exist an EFM (envy-free for mixed goods) and truthful mechanism in general. This impossibility result holds even if there is only one indivisible good and one divisible good and there are only two agents. Thus, we focus on some more restricted settings. Under the setting where agents have binary valuations on indivisible goods and identical valuations on a single divisible good (e.g., money), we design an EFM and truthful mechanism. When agents have binary valuations over both divisible and indivisible goods, we first show there exist EFM and truthful mechanisms when there are only two agents or when there is a single divisible good. On the other hand, we show that the mechanism maximizing Nash welfare cannot ensure EFM and truthfulness simultaneously.","doi":"10.24963/ijcai.2023/313","url":"https://ijcai.org/proceedings/2023/313","pdf":"https://ijcai.org/proceedings/2023/0313.pdf","markdown":"https://ijcai.org/proceedings/2023/313.md","bibtex":"https://ijcai.org/proceedings/2023/bibtex/313","volume":{"slug":"2023","title":"Proceedings of the Thirty-Second International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2023","url":"https://ijcai.org/proceedings/2023/","year":2023,"location":"Macao, SAR","dates":"19-25 August 2023","editors":"Edith Elkind","isbn":"978-1-956792-03-4","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2023"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":313,"pages":{"first":2808,"last":2816},"keywords":["Game Theory and Economic Paradigms: GTEP: Computational social choice","Game Theory and Economic Paradigms: GTEP: Fair division","Game Theory and Economic Paradigms: GTEP: Mechanism design"],"videos":[],"references":[{"position":1,"raw":"[Abdulkadiroglu et al., 2005] Atila Abdulkadiroglu, Parag A. 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