{"type":"ScholarlyArticle","title":"Near-Feasible Stable Matchings with Budget Constraints","authors":[{"name":"Yasushi Kawase","slug":"yasushi-kawase","given":"Yasushi","family":"Kawase","affiliation":"Tokyo Institute of Technology and; RIKEN AIP Center , Tokyo , Japan."},{"name":"Atsushi Iwasaki","slug":"atsushi-iwasaki","given":"Atsushi","family":"Iwasaki","affiliation":"University of Electro-Communications and; RIKEN AIP Center , Tokyo , Japan."}],"abstract":"This paper deals with two-sided matching with budget constraints where one side (firm or hospital) can make monetary transfers (offer wages) to the other (worker or doctor). In a standard model, while multiple doctors can be matched to a single hospital, a hospital has a maximum quota: the number of doctors assigned to a hospital cannot exceed a certain limit. In our model, a hospital instead has a fixed budget: the total amount of wages allocated by each hospital to doctors is constrained. With budget constraints, stable matchings may fail to exist and checking the existence is hard. To deal with the nonexistence of stable matchings, we extend the “matching with contracts” model by Hatfield and Milgrom, so that it handles near-feasible matchings that exceeds each budget of the hospitals by a certain amount. We then propose two novel mechanisms that efficiently return such a near-feasible matching that is stable with respect to the actual amount of wages allocated by each hospital. In particular, by sacrificing strategy-proofness, our second mechanism achieves the best possible bound.","doi":"10.24963/ijcai.2017/35","url":"https://ijcai.org/proceedings/2017/35","pdf":"https://ijcai.org/proceedings/2017/0035.pdf","markdown":"https://ijcai.org/proceedings/2017/35.md","bibtex":"https://ijcai.org/proceedings/2017/bibtex/35","volume":{"slug":"2017","title":"Proceedings of the Twenty-Sixth International Joint Conference on Artificial Intelligence","short_title":"IJCAI 2017","url":"https://ijcai.org/proceedings/2017/","year":2017,"location":"Melbourne, Australia","dates":"19-25 August 2017","editors":"Carles Sierra","isbn":"978-0-9992411-0-3","publisher":"International Joint Conferences on Artificial Intelligence Organization","doi_prefix":"10.24963/ijcai.2017"},"section":"Agent-based and Multi-agent Systems","track":"Main track","number":35,"pages":{"first":242,"last":248},"keywords":["Knowledge Representation, Reasoning, and Logic: Game Theory","Agent-based and Multi-agent Systems: Economic paradigms, auctions and market-based systems"],"videos":[],"references":[{"position":1,"raw":"[Abdulkadiroglu and Sönmez, 2003] Atila Abdulkadiroglu and Tayfun Sönmez. School choice: A mechanism de- sign approach. American Economic Review, 93(3):729- 747, 2003.","title":"Atila Abdulkadiroglu and Tayfun Sönmez. School choice: A mechanism design approach","authors":"Sönmez Abdulkadiroglu","year":"2003","venue":"American Economic Review","doi":null,"url":null,"internal_url":null},{"position":2,"raw":"[Abizada, 2016] Azar Abizada. Stability and incentives for college admissions with budget constraints. Theoretical Economics, 11(2):735-756, 2016.","title":"Stability and incentives for college admissions with budget constraints","authors":"Azar Abizada","year":"2016","venue":"Theoretical Economics","doi":null,"url":null,"internal_url":null},{"position":3,"raw":"[Barberà et al., 2004] Salvador Barberà, Walter Bossert, and Prasanta Pattanaik. Ranking sets of objects. In Handbook of Utility Theory, volume 2. Kluwer Academic Publishers, 2004.","title":"Ranking sets of objects","authors":"Barberà","year":"2004","venue":"Handbook of Utility Theory","doi":null,"url":null,"internal_url":null},{"position":4,"raw":"[Bouveret and Lang, 2011] Sylvain Bouveret and Jérôme Lang. A general elicitation-free protocol for allocating in- divisible goods. In IJCAI, pages 73-78, 2011.","title":"A general elicitation-free protocol for allocating indivisible goods","authors":"Lang ; Bouveret, Sylvain Bouveret, Jérôme Lang","year":"2011","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2011/24"},{"position":5,"raw":"[Budish and Cantillon, 2012] Eric Budish and Estelle Cantil- lon. The multi-unit assignment problem: Theory and ev- idence from course allocation at Harvard. American Eco- nomic Review, 102(5):2237-2271, 2012.","title":"The multi-unit assignment problem: Theory and evidence from course allocation at Harvard","authors":"Cantillon Budish","year":"2012","venue":"American Economic Review","doi":null,"url":null,"internal_url":null},{"position":6,"raw":"[Cygan et al., 2016] Marek Cygan, Łukasz Jeż, and Jiří Sgall. Online knapsack revisited. Theory of Computing Systems, 58(1):153-190, 2016.","title":"Online knapsack revisited","authors":"Cygan","year":"2016","venue":"Theory of Computing Systems","doi":null,"url":null,"internal_url":null},{"position":7,"raw":"[Dantzig, 1957] George Dantzig. Discrete-variable ex- tremum problems. Operations Research, 5(2):266-277, 1957.","title":"Discrete-variable extremum problems","authors":"George Dantzig, Dantzig","year":"1957","venue":"Operations Research","doi":null,"url":null,"internal_url":null},{"position":8,"raw":"[Dean et al., 2006] Brian Dean, Michel Goemans, and Nicole Immorlica. The unsplittable stable marriage prob- lem. In Proceedings of the 5th IFIP International Con- ference on Theoretical Computer Science, pages 65-75, 2006.","title":"The unsplittable stable marriage problem","authors":"Brian Dean, Michel Goemans, Nicole Immorlica","year":"2006","venue":"Proceedings of the 5th IFIP International Conference on Theoretical Computer Science","doi":null,"url":null,"internal_url":null},{"position":9,"raw":"[Drummond and Boutilier, 2013] Joanna Drummond and Craig Boutilier. Elicitation and approximately stable matching with partial preferences. In IJCAI, pages 97-105, 2013.","title":"Elicitation and approximately stable matching with partial preferences","authors":"Boutilier Drummond, Joanna Drummond, Craig Boutilier","year":"2013","venue":"IJCAI","doi":null,"url":null,"internal_url":"/proceedings/2013/26"},{"position":10,"raw":"[Drummond and Boutilier, 2014] Joanna Drummond and Craig Boutilier. Preference elicitation and interview min- imization in stable matchings. In AAAI, pages 645-653, 2014.","title":"Preference elicitation and interview minimization in stable matchings","authors":"Joanna Drummond, Craig Boutilier","year":"2014","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":11,"raw":"[Goto et al., 2016] Masahiro Goto, Atsushi Iwasaki, Yujiro Kawasaki, Ryoji Kurata, Yosuke Yasuda, and Makoto Yokoo. Strategyproof matching with regional minimum and maximum quotas. Artificial Intelligence, 235:40 -57, 2016.","title":"Strategyproof matching with regional minimum and maximum quotas","authors":"Masahiro Goto, Atsushi Iwasaki, Yujiro Kawasaki, Ryoji Kurata, Yosuke Yasuda, Makoto Yokoo","year":"2016","venue":"Artificial Intelligence","doi":null,"url":null,"internal_url":null},{"position":12,"raw":"[Hamada et al., 2017] Naoto Hamada, Anisse Ismaili, Taka- masa Suzuki, and Makoto Yokoo. Weighted matching markets with budget constraints. In AAMAS, pages 317- 325, 2017.","title":"Weighted matching markets with budget constraints","authors":"Naoto Hamada, Anisse Ismaili, Takamasa Suzuki, Makoto Yokoo","year":"2017","venue":"AAMAS","doi":null,"url":null,"internal_url":null},{"position":13,"raw":"[Han et al., 2015] Xin Han, Yasushi Kawase, and Kazuhisa Makino. Randomized algorithms for online knapsack problems. Theoretical Computer Science, 562:395-405, 2015.","title":"Randomized algorithms for online knapsack problems","authors":"Xin Han, Yasushi Kawase, Kazuhisa Makino","year":"2015","venue":"Theoretical Computer Science","doi":null,"url":null,"internal_url":null},{"position":14,"raw":"[Hatfield and Milgrom, 2005] John Hatfield and Paul Mil- grom. Matching with contracts. American Economic Re- view, 95(4):913-935, 2005.","title":"John Hatfield and Paul Milgrom. Matching with contracts","authors":"Milgrom Hatfield","year":"2005","venue":"American Economic Review","doi":null,"url":null,"internal_url":null},{"position":15,"raw":"[Hosseini et al., 2015] Hadi Hosseini, Kate Larson, and Robin Cohen. Matching with dynamic ordinal prefer- ences. In AAAI, pages 936-943, 2015.","title":"Matching with dynamic ordinal preferences","authors":"Hosseini","year":"2015","venue":"AAAI","doi":null,"url":null,"internal_url":null},{"position":16,"raw":"[Iwama and Taketomi, 2002] Kazuo Iwama and Shiro Take- tomi. Removable online knapsack problems. In Proceed- ings of the 29th International Colloquium on Automata, Languages, and Programming (ICALP), pages 293-305, 2002.","title":"Removable online knapsack problems","authors":"Taketomi Iwama, Kazuo Iwama, Shiro Taketomi","year":"2002","venue":"Proceedings of the 29th International Colloquium on Automata, Languages, and Programming (ICALP)","doi":null,"url":null,"internal_url":null},{"position":17,"raw":"[Iwama and Zhang, 2007] Kazuo Iwama and Guochuan Zhang. Optimal resource augmentations for online knap- sack. In Proceedings of the 10th International Work- shop on Approximation Algorithms for Combinatorial Op- timization Problems, pages 180-188, 2007.","title":"Optimal resource augmentations for online knapsack","authors":"Zhang ; ] Kazuo Iwama, Guochuan Iwama, Zhang","year":"2007","venue":"Proceedings of the 10th International Workshop on Approximation Algorithms for Combinatorial Optimization Problems","doi":null,"url":null,"internal_url":null},{"position":18,"raw":"[Kamada and Kojima, 2015] Yuichiro Kamada and Fuhito Kojima. Efficient matching under distributional con- straints: Theory and applications. American Economic Review, 105(1):67-99, 2015.","title":"Efficient matching under distributional constraints: Theory and applications","authors":"Kojima Kamada, Yuichiro Kamada, Fuhito Kojima","year":"2015","venue":"American Economic Review","doi":null,"url":null,"internal_url":null},{"position":19,"raw":"[Kellerer et al., 2004] Hans Kellerer, Ulrich Pferschy, and David Pisinger. Knapsack Problems. Springer, 2004.","title":"Knapsack Problems","authors":"Kellerer","year":"2004","venue":null,"doi":null,"url":null,"internal_url":null},{"position":20,"raw":"[Kelso and Crawford, 1982] Alexander Kelso and Vincent Crawford. Job matching, coalition formation, and gross substitutes. Econometrica, 50(6):1483-1504, 1982.","title":"Job matching, coalition formation, and gross substitutes","authors":"Alexander Kelso, Vincent Crawford","year":"1982","venue":"Econometrica","doi":null,"url":null,"internal_url":null},{"position":21,"raw":"[Kojima et al., 2013] Fuhito Kojima, Parag Pathak, and Alvin Roth. Matching with couples: Stability and in- centives in large markets. The Quarterly Journal of Eco- nomics, 128(4):1585-1632, 2013.","title":"Matching with couples: Stability and incentives in large markets","authors":"Kojima","year":"2013","venue":"The Quarterly Journal of Economics","doi":null,"url":null,"internal_url":null},{"position":22,"raw":"[Kurata et al., 2017] Ryoji Kurata, Naoto Hamada, Atsushi Iwasaki, and Makoto Yokoo. Controlled school choice with soft bounds and overlapping types. Journal of Ar- tificial Intelligence Research, 58:153-184, 2017.","title":"Controlled school choice with soft bounds and overlapping types","authors":"Ryoji Kurata, Naoto Hamada, Atsushi Iwasaki, Makoto Yokoo","year":"2017","venue":"Journal of Artificial Intelligence Research","doi":null,"url":null,"internal_url":null},{"position":23,"raw":"[Manlove, 2013] David Manlove. Algorithmics of Matching Under Preferences. World Scientific Publishing Company, 2013.","title":"Algorithmics of Matching Under Preferences","authors":"David Manlove","year":"2013","venue":null,"doi":null,"url":null,"internal_url":null},{"position":24,"raw":"[McDermid and Manlove, 2010] Eric McDermid and David Manlove. Keeping partners together: algorithmic results for the hospitals/residents problem with couples. Journal of Combinatorial Optimization, 19:279-303, 2010.","title":"Keeping partners together: algorithmic results for the hospitals/residents problem with couples","authors":"Manlove Mcdermid, Eric Mcdermid, David Manlove","year":"2010","venue":"Journal of Combinatorial Optimization","doi":null,"url":null,"internal_url":null},{"position":25,"raw":"[Mongell and Roth, 1986] Susan Mongell and Alvin Roth. A note on job matching with budget constraints. Economics Letters, 21(2):135-138, 1986.","title":"Susan Mongell and Alvin Roth. A note on job matching with budget constraints","authors":"Roth Mongell","year":"1986","venue":"Economics Letters","doi":null,"url":null,"internal_url":null},{"position":26,"raw":"[Nguyen and Vohra, 2015] Thanh Nguyen and Rakesh Vohra. Near feasible stable matchings. In Proceed- ings of the 16th ACM Conference on Economics and Computation, pages 41-42, 2015.","title":"Near feasible stable matchings","authors":"Thanh Nguyen, Rakesh Vohra","year":"2015","venue":"Proceedings of the 16th ACM Conference on Economics and Computation","doi":null,"url":null,"internal_url":null},{"position":27,"raw":"[Perrault et al., 2016] Andrew Perrault, Joanna Drummond, and Fahiem Bacchus. Strategy-proofness in the stable matching problem with couples. In AAMAS, pages 132- 140, 2016.","title":"Strategy-proofness in the stable matching problem with couples","authors":"Andrew Perrault, Joanna Drummond, Fahiem Bacchus","year":"2016","venue":"AAMAS","doi":null,"url":null,"internal_url":null},{"position":28,"raw":"[Roth and Sotomayor, 1990] Alvin Roth and Marilda So- tomayor. Two-Sided Matching: A Study in Game- Theoretic Modeling and Analysis. Cambridge University Press, 1990.","title":"Alvin Roth and Marilda Sotomayor. Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis","authors":"Sotomayor Roth","year":"1990","venue":null,"doi":null,"url":null,"internal_url":null}],"license_note":"Copyright International Joint Conferences on Artificial Intelligence."}