Finding all stable matchings with couples

In two-sided matching markets in which some doctors form couples, a stable matching does not necessarily exist.Wecharacterize the set of stable matchings as the fixed points of a function that is reminiscent of a tâtonnement process. Then we show that this function ismonotone decreasing with respect to a certain partialorder. Based on these results,wepresent an algorithm that finds all the stable matchings wheneverone exists, and otherwise demonstrates that there is no stable matching.

[1]  Makoto Yokoo,et al.  Strategyproof Matching with Minimum Quotas , 2016, TEAC.

[2]  Tamás Fleiner,et al.  Matching couples with Scarf’s algorithm , 2015, Annals of Mathematics and Artificial Intelligence.

[3]  Thanh Nguyen,et al.  Near Feasible Stable Matchings with Complementarities , 2014 .

[4]  Itai Ashlagi,et al.  Stability in Large Matching Markets with Complementarities , 2014, Oper. Res..

[5]  Makoto Yokoo,et al.  Strategy-proof matching with regional minimum quotas , 2014, AAMAS.

[6]  David Manlove,et al.  The Hospitals / Residents Problem with Couples: Complexity and Integer Programming Models , 2013, SEA.

[7]  Flip Klijn,et al.  Matching with couples: a Multidisciplinary Survey , 2013, IGTR.

[8]  L. S. Shapley,et al.  College Admissions and the Stability of Marriage , 2013, Am. Math. Mon..

[9]  F. Kojima,et al.  Stability and Strategy-Proofness for Matching with Constraints: A Problem in the Japanese Medical Match and Its Solution , 2012 .

[10]  Leonid Boytsov,et al.  Indexing methods for approximate dictionary searching: Comparative analysis , 2011, JEAL.

[11]  Robert W. Irving,et al.  Stable matching with couples: An empirical study , 2011, JEAL.

[12]  Parag A. Pathak,et al.  School Admissions Reform in Chicago and England: Comparing Mechanisms by Their Vulnerability to Manipulation , 2011 .

[13]  M. Pycia.  Stability and Preference Alignment in Matching and Coalition Formation , 2010 .

[14]  Onur Kesten.  School Choice with Consent , 2010 .

[15]  David Manlove,et al.  The College Admissions problem with lower and common quotas , 2010, Theor. Comput. Sci..

[16]  Parag A. Pathak,et al.  Matching with Couples: Stability and Incentives in Large Markets , 2010 .

[17]  D. Manlove,et al.  Keeping partners together: algorithmic results for the hospitals/residents problem with couples , 2010, J. Comb. Optim..

[18]  Yeon-Koo Che,et al.  Resolving Conflicting Preferences in School Choice: The 'Boston' Mechanism Reconsidered , 2009 .

[19]  Parag A. Pathak,et al.  Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match , 2009 .

[20]  Yeon-Koo Che,et al.  Asymptotic Equivalence of Probabilistic Serial and Random Priority Mechanisms , 2008 .

[21]  Parag A. Pathak,et al.  Leveling the Playing Field: Sincere and Sophisticated Players in the Boston Mechanism , 2008 .

[22]  Aytek Erdil,et al.  What's the Matter with Tie-Breaking? Improving Efficiency in School Choice , 2008 .

[23]  F. Kojima,et al.  Matching with Contracts: Comment , 2008 .

[24]  M. Utku Ünver,et al.  Course Bidding at Business Schools , 2007 .

[25]  Federico Echenique,et al.  Finding all equilibria in games of strategic complements , 2007, J. Econ. Theory.

[26]  M. Utku Ünver,et al.  Credible group stability in many-to-many matching problems , 2006, J. Econ. Theory.

[27]  Federico Echenique,et al.  A Solution to Matching with Preferences Over Colleagues , 2005, Games Econ. Behav..

[28]  Paul R. Milgrom,et al.  Matching with Contracts , 2005 .

[29]  Parag A. Pathak,et al.  The Boston Public School Match , 2005 .

[30]  Parag A. Pathak,et al.  The New York City High School Match , 2005 .

[31]  M. Ostrovsky.  Stability in Supply Chain Networks , 2005 .

[32]  Nicole Immorlica,et al.  Marriage, honesty, and stability , 2005, SODA '05.

[33]  F. Echenique,et al.  A Theory of Stability in Many-to-Many Matching Markets , 2004 .

[34]  M. Utku Ünver,et al.  Credible Group Stability in Multi-Partner Matching Problems , 2004 .

[35]  Atila Abdulkadiroglu,et al.  School Choice: A Mechanism Design Approach , 2003 .

[36]  Tamás Fleiner,et al.  A Fixed-Point Approach to Stable Matchings and Some Applications , 2003, Math. Oper. Res..

[37]  Hiroyuki Adachi.  On a characterization of stable matchings , 2000 .

[38]  Marilda Sotomayor.  Three remarks on the many-to-many stable matching problem , 1999 .

[39]  A. Roth,et al.  The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design , 1999, The American economic review.

[40]  Bhaskar Dutta,et al.  Stability of matchings when individuals have preferences over colleagues , 1997 .

[41]  Marilda Sotomayor,et al.  A Non-constructive Elementary Proof of the Existence of Stable Marriages , 1996 .

[42]  A. Roth.  A natural experiment in the organization of entry-level labor markets: regional markets for new physicians and surgeons in the United Kingdom. , 1991, The American economic review.

[43]  Eytan Ronn,et al.  NP-Complete Stable Matching Problems , 1990, J. Algorithms.

[44]  A. Roth.  On the Allocation of Residents to Rural Hospitals: A General Property of Two-Sided Matching Markets , 1986 .

[45]  David Gale,et al.  Some remarks on the stable matching problem , 1985, Discret. Appl. Math..

[46]  David Gale,et al.  Ms. Machiavelli and the Stable Matching Problem , 1985 .

[47]  A. Roth.  The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory , 1984, Journal of Political Economy.

[48]  L. B. Wilson,et al.  Stable marriage assignment for unequal sets , 1970 .

[49]  F. Kojima,et al.  Efficient Matching under Distributional Constraints: Theory and Applications , 2015 .

[50]  Parag A. Pathak,et al.  Incentives and Stability in Large Two-Sided Matching Markets , 2007 .

[51]  Bettina Klaus,et al.  Paths to stability for matching markets with couples , 2007, Games Econ. Behav..

[52]  Bettina Klaus,et al.  Corrigendum: Stable Matchings and Preferences of Couples , 2007 .

[53]  C. Plott,et al.  Supplement to: Core Many-to-One Matchings by Fixed-Point Methods , 2004 .

[54]  Marilda Sotomayor,et al.  Implementation in the many-to-many matching market , 2004, Games Econ. Behav..

[55]  M. Balinski,et al.  A Tale of Two Mechanisms: Student Placement , 1999 .

[56]  A. Roth,et al.  Two-Sided Matching: A Study in Game-Theoretic Modeling and Analysis , 1990 .

[57]  F. Klijn,et al.  Centre De Referència En Economia Analítica Barcelona Economics Working Paper Series Working Paper Nº 117 Stable Matchings and Preferences of Couples , 2022 .

[58]  Bettina Klaus,et al.  Centre De Referència En Economia Analítica Barcelona Economics Working Paper Series Working Paper Nº 78 Some Things Couples Always Wanted to Know about Stable Matchings (but Were Afraid to Ask) , 2022 .