{"type":"ScholarlyArticle","title":"An EF2X Allocation Protocol for Restricted Additive Valuations","authors":[{"name":"Hannaneh Akrami","slug":"hannaneh-akrami","given":"Hannaneh","family":"Akrami","affiliation":"Max Planck Institute for Informatics; Graduiertenschule Informatik , Universität des Saarlandes"},{"name":"Rojin Rezvan","slug":"rojin-rezvan","given":"Rojin","family":"Rezvan","affiliation":"University of Texas at Austin , Computer Science Department"},{"name":"Masoud Seddighin","slug":"masoud-seddighin","given":"Masoud","family":"Seddighin","affiliation":"School of Computer Science , Institute for Research in Fundamental Sciences (IPM) , P. O. Box: 19395 - 5746 , Tehran , Iran"}],"abstract":"We study the problem of fairly allocating a set of indivisible goods to a set of n agents.  Envy-freeness up to any good (EFX) criterion (which \r\nrequires that no agent prefers the bundle of another agent after the removal of any single good) is known to be a remarkable analogue of envy-freeness when the resource is a set of indivisible goods.\r\nIn this paper, we investigate EFX  for restricted additive valuations, that is, every good has a non-negative value, and every agent is interested in only some of the goods.\r\n\r\nWe introduce a natural relaxation of EFX called EFkX which requires that no agent envies another agent after the removal of any k goods. Our main contribution is an algorithm that finds a complete (i.e., no good is discarded) EF2X allocation for restricted additive valuations. In our algorithm we devise new concepts, namely configuration and envy-elimination that might be of independent interest. \r\n\r\nWe also use our new tools to find an EFX allocation for restricted additive valuations that discards at most n/2 -1 goods.","doi":"10.24963/ijcai.2022/3","url":"https://ijcai.org/proceedings/2022/3","pdf":"https://ijcai.org/proceedings/2022/0003.pdf","markdown":"https://ijcai.org/proceedings/2022/3.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/3","volume":{"slug":"2022","title":"Proceedings of the Thirty-First International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2022","url":"https://ijcai.org/proceedings/2022/","year":2022,"location":"Vienna","dates":"23-29 July 2022","editors":"Luc De Raedt","isbn":"978-1-956792-00-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2022"},"section":"Agent-based and Multi-agent Systems","track":"Main Track","number":3,"pages":{"first":17,"last":23},"keywords":["Agent-based and Multi-agent Systems: Algorithmic Game Theory","AI Ethics, Trust, Fairness: Fairness & Diversity"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38986920","length_sec":87,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38985063","length_sec":355,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Amanatidis et al., 2020] Georgios Amanatidis, Evangelos Markakis, and Apostolos Ntokos. 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