{"type":"ScholarlyArticle","title":"Probabilistic Analysis of Stable Matching in Large Markets with Siblings","authors":[{"name":"Zhaohong Sun","slug":"zhaohong-sun","given":"Zhaohong","family":"Sun","affiliation":""},{"name":"Tomohiko Yokoyama","slug":"tomohiko-yokoyama","given":"Tomohiko","family":"Yokoyama","affiliation":""},{"name":"Makoto Yokoo","slug":"makoto-yokoo","given":"Makoto","family":"Yokoo","affiliation":""}],"abstract":"We study a practical centralized matching problem which assigns children to daycare centers.\r\nThe collective preferences of siblings from the same family introduce complementarities, which can lead to the absence of stable matchings, as observed in the hospital-doctor matching problems involving couples. Intriguingly, stable matchings are consistently observed in real-world daycare markets, despite the prevalence of sibling applicants.\r\n\r\nWe conduct a probabilistic analysis of large random markets to examine the existence of stable matchings in such markets. Specifically, we focus on scenarios where daycare centers have similar priorities over children, a common characteristic in real-world markets. Our analysis reveals that as the market size approaches infinity, the likelihood of stable matchings existing converges to 1.\r\n\r\nTo facilitate our exploration, we refine an existing heuristic algorithm to address a more rigorous stability concept, as the original one may fail to meet this criterion. Through extensive experiments on both real-world and synthetic datasets, we demonstrate the effectiveness of our revised algorithm in identifying stable matchings, particularly when daycare priorities exhibit high similarity.","doi":"10.24963/ijcai.2025/453","url":"https://ijcai.org/proceedings/2025/453","pdf":"https://ijcai.org/proceedings/2025/0453.pdf","markdown":"https://ijcai.org/proceedings/2025/453.md","bibtex":"https://ijcai.org/proceedings/2025/bibtex/453","volume":{"slug":"2025","title":"Proceedings of the Thirty-Fourth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2025","url":"https://ijcai.org/proceedings/2025/","year":2025,"location":"Montreal, Canada","dates":"16-22 August 2025","editors":"James Kwok","isbn":"978-1-956792-06-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2025"},"section":"Game Theory and Economic Paradigms","track":"Main Track","number":453,"pages":{"first":4065,"last":4072},"keywords":["Game Theory and Economic Paradigms: GTEP: Auctions and market-based systems"],"videos":[],"references":[],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}