{"type":"ScholarlyArticle","title":"The Dichotomous Affiliate Stable Matching Problem: Approval-Based Matching with Applicant-Employer Relations","authors":[{"name":"Marina Knittel","slug":"marina-knittel","given":"Marina","family":"Knittel","affiliation":"Computer Science Department , University of Maryland"},{"name":"Samuel Dooley","slug":"samuel-dooley","given":"Samuel","family":"Dooley","affiliation":"Computer Science Department , University of Maryland"},{"name":"John Dickerson","slug":"john-dickerson","given":"John","family":"Dickerson","affiliation":"Computer Science Department , University of Maryland"}],"abstract":"While the stable marriage problem and its variants model a vast range of matching markets, they fail to capture complex agent relationships, such as the affiliation of applicants and employers in an interview marketplace. To model this problem, the existing literature on matching with externalities permits agents to provide complete and total rankings over matchings based off of both their own and their affiliates' matches. This complete ordering restriction is unrealistic, and further the model may have an empty core. To address this, we introduce the Dichotomous Affiliate Stable Matching (DASM) Problem, where agents' preferences indicate dichotomous acceptance or rejection of another agent in the marketplace, both for themselves and their affiliates. We also assume the agent's preferences over entire matchings are determined by a general weighted valuation function of their (and their affiliates') matches. Our results are threefold: (1) we use a human study to show that real-world matching rankings follow our assumed valuation function; (2) we prove that there always exists a stable solution by providing an efficient, easily-implementable algorithm that finds such a solution; and (3) we experimentally validate the efficiency of our algorithm versus a linear-programming-based approach.","doi":"10.24963/ijcai.2022/51","url":"https://ijcai.org/proceedings/2022/51","pdf":"https://ijcai.org/proceedings/2022/0051.pdf","markdown":"https://ijcai.org/proceedings/2022/51.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/51","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":51,"pages":{"first":356,"last":362},"keywords":["Agent-based and Multi-agent Systems: Economic Paradigms, Auctions and Market-Based Systems","Agent-based and Multi-agent Systems: Mechanism Design"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38986763","length_sec":75,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38984906","length_sec":364,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Ashlagi and Roth, 2021] Itai Ashlagi and Alvin E Roth. 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