{"type":"ScholarlyArticle","title":"Tolerance is Necessary for Stability: Single-Peaked Swap Schelling Games","authors":[{"name":"Davide Bilò","slug":"davide-bilo","given":"Davide","family":"Bilò","affiliation":"University of Sassari , Italy"},{"name":"Vittorio Bilò","slug":"vittorio-bilo","given":"Vittorio","family":"Bilò","affiliation":"University of Salento , Italy"},{"name":"Pascal Lenzner","slug":"pascal-lenzner","given":"Pascal","family":"Lenzner","affiliation":"Hasso Plattner Institute , University of Potsdam , Germany"},{"name":"Louise Molitor","slug":"louise-molitor","given":"Louise","family":"Molitor","affiliation":"Hasso Plattner Institute , University of Potsdam , Germany"}],"abstract":"Residential segregation in metropolitan areas is a phenomenon that can be observed all over the world. Recently, this was investigated via game-theoretic models. There, selfish agents of two types are equipped with a monotone utility function that ensures higher utility if an agent has more same-type neighbors. The agents strategically choose their location on a given graph that serves as residential area to maximize their utility. However, sociological polls suggest that real-world agents are actually favoring mixed-type neighborhoods, and hence should be modeled via non-monotone utility functions. To address this, we study Swap Schelling Games with single-peaked utility functions. Our main finding is that tolerance, i.e., agents favoring fifty-fifty neighborhoods or being in the minority, is necessary for equilibrium existence on almost regular or bipartite graphs. Regarding the quality of equilibria, we derive (almost) tight bounds on the Price of Anarchy and the Price of Stability. In particular, we show that the latter is constant on bipartite and almost regular graphs.","doi":"10.24963/ijcai.2022/12","url":"https://ijcai.org/proceedings/2022/12","pdf":"https://ijcai.org/proceedings/2022/0012.pdf","markdown":"https://ijcai.org/proceedings/2022/12.md","bibtex":"https://ijcai.org/proceedings/2022/bibtex/12","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":12,"pages":{"first":81,"last":87},"keywords":["Agent-based and Multi-agent Systems: Algorithmic Game Theory","Agent-based and Multi-agent Systems: Noncooperative Games"],"videos":[{"label":"Video #1","url":"https://slideslive.com/38986860","length_sec":84,"provider":"slideslive"},{"label":"Video #2","url":"https://slideslive.com/38985003","length_sec":353,"provider":"slideslive"}],"references":[{"position":1,"raw":"[Acevedo-Garcia and Lochner, 2003] Dolores Acevedo- Garcia and Kimberly A. 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