{"type":"ScholarlyArticle","title":"Stable Roommate Problem with Diversity Preferences","authors":[{"name":"Niclas Boehmer","slug":"niclas-boehmer","given":"Niclas","family":"Boehmer","affiliation":"TU Berlin , Berlin , Germany; University of Oxford."},{"name":"Edith Elkind","slug":"edith-elkind","given":"Edith","family":"Elkind","affiliation":"University of Oxford , Oxford , UK"}],"abstract":"In the multidimensional stable roommate problem, agents have to be allocated to rooms and have preferences over sets of potential roommates. We study the complexity of finding good allocations of agents to rooms under the assumption that agents have diversity preferences (Bredereck, Elkind, Igarashi, AAMAS'19): each agent belongs to one of the two types (e.g., juniors and seniors, artists and engineers), and agents’ preferences over rooms depend solely on the fraction of agents of their own type among their potential roommates. We consider various solution concepts for this setting, such as core and exchange stability, Pareto optimality and envy-freeness. On the negative side, we prove that envy-free, core stable or (strongly) exchange stable outcomes may fail to exist and that the associated decision problems are NP-complete. On the positive side, we show that these problems are in FPT with respect to the room size, which is not the case for the general stable roommate problem.","doi":"10.24963/ijcai.2020/14","url":"https://ijcai.org/proceedings/2020/14","pdf":"https://ijcai.org/proceedings/2020/0014.pdf","markdown":"https://ijcai.org/proceedings/2020/14.md","bibtex":"https://ijcai.org/proceedings/2020/bibtex/14","volume":{"slug":"2020","title":"Proceedings of the Twenty-Ninth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2020","url":"https://ijcai.org/proceedings/2020/","year":2020,"location":"Yokohama","dates":"January 2021 (postponed from 11-17 July 2020)","editors":"Christian Bessiere","isbn":"978-0-9992411-6-5","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2020"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":14,"pages":{"first":96,"last":102},"keywords":["Agent-based and Multi-agent Systems: Computational Social Choice","Agent-based and Multi-agent Systems: Cooperative Games"],"videos":[{"label":"Video","url":"https://videos.ijcai20.org/25115/file_25115.m3u8","length_sec":297,"provider":"hls"}],"references":[{"position":1,"raw":"[Abdulkadiroglu and Sönmez, 2003] Atila Abdulkadiroglu and Tayfun Sönmez. School choice: A mechanism design approach. Am Econ Rev, 93(3):729-747, 2003.","title":"Atila Abdulkadiroglu and Tayfun Sönmez. School choice: A mechanism design approach","authors":"Sönmez Abdulkadiroglu","year":"2003","venue":"Am Econ Rev","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Abraham et al., 2005] David J. Abraham, Péter Biró, and David Manlove. \"Almost stable\" matchings in the room- mates problem. In WAOA'05, pages 1-14, 2005.","title":"Almost stable\" matchings in the roommates problem","authors":"David J Abraham, Péter Biró, David Manlove","year":"2005","venue":"WAOA'05","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Abraham et al., 2007] David J Abraham, Ariel Levavi, David F Manlove, and Gregg O'Malley. The stable room- mates problem with globally-ranked pairs. In WINE'07, pages 431-444, 2007.","title":"The stable roommates problem with globally-ranked pairs","authors":"J David, Ariel Abraham, David F Levavi, Gregg O' Manlove, Malley","year":"2007","venue":"WINE'07","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Alcalde, 1994] José Alcalde. Exchange-proofness or divorce-proofness? Stability in one-sided matching mar- kets. Econ Des, 1(1):275-287, 1994.","title":"José Alcalde. Exchange-proofness or divorce-proofness? Stability in one-sided matching markets","authors":"Alcalde","year":"1994","venue":"Econ Des","doi":null,"url":null,"internal_url":null},{"position":5,"raw":"[Aziz and Klaus, 2019] Haris Aziz and Bettina Klaus. Ran- dom matching under priorities: Stability and no envy con- cepts. Soc Choice Welf, 53(2):213-259, 2019.","title":"Random matching under priorities: Stability and no envy concepts","authors":"Haris Aziz, Bettina Klaus","year":"2019","venue":"Soc Choice Welf","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Aziz et al., 2013] Haris Aziz, Felix Brandt, and Paul Har- renstein. Pareto optimality in coalition formation. Games Econ Behav, 82:562-581, 2013.","title":"Pareto optimality in coalition formation","authors":"Haris Aziz, Felix Brandt, Paul Harrenstein","year":"2013","venue":"Games Econ Behav","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Aziz et al., 2019] Haris Aziz, Florian Brandl, Felix Brandt, Paul Harrenstein, Martin Olsen, and Dominik Peters. Frac- tional hedonic games. ACM Trans Econ Comput, 7(2):6:1- 6:29, 2019.","title":"Fractional hedonic games","authors":"Haris Aziz, Florian Brandl, Felix Brandt, Paul Harrenstein, Martin Olsen, Dominik Peters","year":"2019","venue":"ACM Trans Econ Comput","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Ballester, 2004] Coralio Ballester. NP-completeness in he- donic games. Games Econ Behav, 49:1-30, 2004.","title":"Coralio Ballester. NP-completeness in hedonic games","authors":"Ballester","year":"2004","venue":"Games Econ Behav","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Banerjee et al., 2001] Suryapratim Banerjee, Hideo Kon- ishi, and Tayfun Sönmez. Core in a simple coalition for- mation game. Soc Choice Welf, 18(1):135-153, 2001.","title":"Core in a simple coalition formation game","authors":"Banerjee","year":"2001","venue":"Soc Choice Welf","doi":null,"url":null,"internal_url":null},{"position":10,"raw":"[Bartholdi III and Trick, 1986] John Bartholdi III and Michael A Trick. Stable matching with preferences derived from a psychological model. Oper Res Lett, 5(4):165-169, 1986.","title":"John Bartholdi III and Michael A Trick. Stable matching with preferences derived from a psychological model","authors":"Iii Bartholdi, Trick","year":"1986","venue":"Oper Res Lett","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Boehmer and Elkind, 2020a] Niclas Boehmer and Edith Elkind. Individual-based stability in hedonic diversity games. In AAAI'20, 2020.","title":"Individual-based stability in hedonic diversity games","authors":"Elkind Boehmer, Niclas Boehmer, Edith Elkind","year":"2020","venue":"AAAI'20","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Boehmer and Elkind, 2020b] Niclas Boehmer and Edith Elkind. Stable roommate problem with diversity prefer- ences, 2020. arXiv 2004.14640.","title":"Stable roommate problem with diversity preferences","authors":"Elkind Boehmer, Niclas Boehmer, Edith Elkind","year":"2020","venue":null,"doi":null,"url":null,"internal_url":null},{"position":13,"raw":"Anna Bogomolnaia and Matthew O Jackson. The stability of hedonic coalition structures. Games Econ Behav, 38(2):201-230, 2002.","title":"The stability of hedonic coalition structures","authors":"Anna Bogomolnaia, Matthew O Jackson","year":"2002","venue":"Games Econ Behav","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Bredereck et al., 2017] Robert Bredereck, Jiehua Chen, Ugo Paavo Finnendahl, and Rolf Niedermeier. Stable roommate with narcissistic, single-peaked, and single- crossing preferences. In ADT'17, pages 315-330, 2017.","title":"Stable roommate with narcissistic, single-peaked, and singlecrossing preferences","authors":"Robert Bredereck, Jiehua Chen, Ugo Paavo Finnendahl, Rolf Niedermeier","year":"2017","venue":"ADT'17","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Bredereck et al., 2019] Robert Bredereck, Edith Elkind, and Ayumi Igarashi. Hedonic diversity games. In AA- MAS'19, pages 565-573, 2019.","title":"Hedonic diversity games","authors":"Robert Bredereck, Edith Elkind, Ayumi Igarashi","year":"2019","venue":"AA-MAS'19","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Cechlárová and Manlove, 2005] Katarína Cechlárová and David F Manlove. The exchange-stable marriage problem. Discrete Appl Math, 152(1-3):109-122, 2005.","title":"The exchange-stable marriage problem","authors":"Manlove Cechlárová, Katarína Cechlárová, David F Manlove","year":"2005","venue":"Discrete Appl Math","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Chung, 2000] Kim-Sau Chung. On the existence of stable roommate matchings. Games Econ Behav, 33(2):206-230, 2000.","title":"On the existence of stable roommate matchings","authors":"Chung, Kim-Sau Chung","year":"2000","venue":"Games Econ Behav","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Cseh and Juhos, 2019] Ágnes Cseh and Attila Juhos. Pair- wise preferences in the stable marriage problem. In STACS'19, pages 21:1-21:16, 2019.","title":"Pairwise preferences in the stable marriage problem","authors":"Juhos Cseh, Ágnes Cseh, Attila Juhos","year":"2019","venue":"STACS'19","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Cseh et al., 2019] Ágnes Cseh, Tamás Fleiner, and Petra Harján. Pareto optimal coalitions of fixed size, 2019. arXiv 1901.06737.","title":"Pareto optimal coalitions of fixed size","authors":"Ágnes Cseh, Tamás Fleiner, Petra Harján","year":"2019","venue":null,"doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Elkind et al., 2016] Edith Elkind, Angelo Fanelli, and Michele Flammini. Price of Pareto optimality in hedonic games. In AAAI'16, pages 475-481, 2016.","title":"Price of Pareto optimality in hedonic games","authors":"Elkind","year":"2016","venue":"AAAI'16","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Gale and Shapley, 1962] David Gale and Lloyd S Shapley. College admissions and the stability of marriage. Am Math Mon, 69(1):9-15, 1962.","title":"College admissions and the stability of marriage","authors":"Shapley Gale","year":"1962","venue":"Am Math Mon","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Hofbauer, 2016] Johannes Hofbauer. d-dimensional stable matching with cyclic preferences. Math Soc Sci, 82:72- 76, 2016.","title":"Johannes Hofbauer. d-dimensional stable matching with cyclic preferences","authors":"Hofbauer","year":"2016","venue":"Math Soc Sci","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Huang, 2007] Chien-Chung Huang. Two's company, three's a crowd: Stable family and threesome roommates prob- lems. In ESA'07, pages 558-569, 2007.","title":"Two's company, three's a crowd: Stable family and threesome roommates problems","authors":"Chien-Chung Huang","year":"2007","venue":"ESA'07","doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[Huang, 2010] Chien-Chung Huang. Classified stable matching. In SODA'10, pages 1235-1253, 2010.","title":"Classified stable matching","authors":"Chien-Chung Huang","year":"2010","venue":"SODA'10","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Irving, 1985] Robert W Irving. An efficient algorithm for the \"stable roommates\" problem. J Algorithms, 6(4):577- 595, 1985.","title":"An efficient algorithm for the \"stable roommates\" problem","authors":"Irving Robert","year":"1985","venue":"J Algorithms","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Iwama et al., 2007] Kazuo Iwama, Shuichi Miyazaki, and Kazuya Okamoto. Stable roommates problem with triple rooms. In WAAC'07, pages 105-112, 2007.","title":"Stable roommates problem with triple rooms","authors":"Kazuo Iwama, Shuichi Miyazaki, Kazuya Okamoto","year":"2007","venue":"WAAC'07","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Kamada and Kojima, 2015] Yuichiro Kamada and Fuhito Kojima. Efficient matching under distributional con- straints: Theory and applications. Am Econ Rev, 105(1):67-99, 2015.","title":"Efficient matching under distributional constraints: Theory and applications","authors":"Kojima Kamada, Yuichiro Kamada, Fuhito Kojima","year":"2015","venue":"Am Econ Rev","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Lenstra Jr, 1983] Hendrik W. Lenstra Jr. Integer program- ming with a fixed number of variables. Math Oper Res, 8(4):538-548, 1983.","title":"Integer programming with a fixed number of variables","authors":"Hendrik W Lenstra","year":"1983","venue":"Math Oper Res","doi":null,"url":null,"internal_url":null},{"position":29,"raw":"[Morrill, 2010] Thayer Morrill. The roommates problem re- visited. J Econ Theory, 145(5):1739-1756, 2010.","title":"The roommates problem revisited","authors":"Thayer Morrill","year":"2010","venue":"J Econ Theory","doi":null,"url":null,"internal_url":null},{"position":30,"raw":"[Ng and Hirschberg, 1991] Cheng Ng and Daniel S Hirschberg. Three-dimensional stable matching problems. SIAM J Discrete Math, 4(2):245-252, 1991.","title":"Three-dimensional stable matching problems","authors":"Cheng Ng, Daniel S Hirschberg","year":"1991","venue":"SIAM J Discrete Math","doi":null,"url":null,"internal_url":null},{"position":31,"raw":"[Peters, 2016] Dominik Peters. Complexity of hedonic games with dichotomous preferences. In AAAI'16, pages 579-585, 2016.","title":"Complexity of hedonic games with dichotomous preferences","authors":"Dominik Peters, Peters","year":"2016","venue":"AAAI'16","doi":null,"url":null,"internal_url":null},{"position":32,"raw":"[Ronn, 1990] Eytan Ronn. NP-complete stable matching problems. J Algorithms, 11(2):285-304, 1990.","title":"NP-complete stable matching problems","authors":"Eytan Ronn","year":"1990","venue":"J Algorithms","doi":null,"url":null,"internal_url":null},{"position":33,"raw":"[Salovey and Rodin, 1984] Peter Salovey and Judith Rodin. Some antecedents and consequences of social-comparison jealousy. J Pers Soc Psychol, 47(4):780, 1984.","title":"Some antecedents and consequences of social-comparison jealousy","authors":"Rodin Salovey, Peter Salovey, Judith Rodin","year":"1984","venue":"J Pers Soc Psychol","doi":null,"url":null,"internal_url":null},{"position":34,"raw":"[Sotomayor, 2011] Marilda Sotomayor. The Pareto-stability concept is a natural solution concept for discrete match- ing markets with indifferences. Int J Game Theory, 40(3):631-644, 2011.","title":"The Pareto-stability concept is a natural solution concept for discrete matching markets with indifferences","authors":"Marilda Sotomayor","year":"2011","venue":"Int J Game Theory","doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}