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Stable matchings and preferences of couples. (English) Zbl 1098.91092
J. Econ. Theory 121, No. 1, 75-106 (2005); corrections ibid. 144, No. 5, 2227-2233 (2009).
Summary: Couples looking for jobs in the same labor market may cause instabilities. We determine a natural preference domain, the domain of weakly responsive preferences, that guarantees stability. Under a restricted unemployment aversion condition we show that this domain is maximal for the existence of stable matchings. We illustrate how small deviations from (weak) responsiveness, that model the wish of couples to be closer together, cause instability, even when we use a weaker stability notion that excludes myopic blocking. Our remaining results deal with various properties of the set of stable matchings for “responsive couples markets”, viz., optimality, filled positions, and manipulation.

91B68 Matching models
91B08 Individual preferences
91B40 Labor market, contracts (MSC2010)
Full Text: DOI
[1] A. Abdulkadiroğlu, College admissions with affirmative action, Working paper, Department of Economics, Columbia University, May 2003.
[2] Aldershof, B.; Carducci, O.M., Stable matchings with couples, Discrete appl. math., 68, 203-207, (1996) · Zbl 0846.90089
[3] Alkan, A.; Gale, D., Stable schedule matching under revealed preferences, J. econ. theory, 112, 289-306, (2003) · Zbl 1068.91059
[4] D. Cantala, Matching markets: the particular case of couples, Working paper, Centro de Estudios Económicos, El Colegio de México, April 2004. · Zbl 1079.91060
[5] Dubins, L.E.; Freedman, D.A., Machiavelli and the gale – shapley algorithm, Amer. math. mon., 88, 485-494, (1981) · Zbl 0449.92024
[6] Gale, D.; Shapley, L.S., College admissions and the stability of marriage, Amer. math. mon., 69, 9-15, (1962) · Zbl 0109.24403
[7] J.W. Hatfield, P. Milgrom, Auctions, matching and the law of aggregate demand, Working paper 04-003, Department of Economics, Stanford University, February 2004.
[8] Kelso, A.S.; Crawford, V.P., Job matching, coalition formation, and Gross substitutes, Econometrica, 50, 1483-1504, (1982) · Zbl 0503.90019
[9] B. Klaus, F. Klijn, J. Massó, Some things couples always wanted to know about stable matchings (but were afraid to ask), Working paper, Departament d’Economia i d’Història Econòmica, Universitat Autònoma de Barcelona, September 2003.
[10] Klijn, F.; Massó, J., Weak stability and a bargaining set for the marriage model, Games econ. behav., 42, 91-100, (2003) · Zbl 1032.91095
[11] Knuth, D.E., Marriages stables, (1976), Les Presses de l’Université Montreal
[12] Martı́nez, R.; Massó, J.; Neme, A.; Oviedo, J., Single agents and the set of many-to-one stable matchings, J. econ. theory, 91, 91-105, (2000) · Zbl 0955.91048
[13] McVitie, D.G.; Wilson, L.B., Stable marriage assignments for unequal sets, Bit, 10, 295-309, (1970) · Zbl 0225.05002
[14] Ronn, E., NP-complete stable matching problems, J. algorithms, 11, 285-304, (1990) · Zbl 0705.68065
[15] Roth, A.E., The economics of matchingstability and incentives, Math. operations res., 7, 617-628, (1982) · Zbl 0496.90008
[16] Roth, A.E., The evolution of the labor market for medical interns and residentsa case study in game theory, J. polit. econ., 92, 991-1016, (1984)
[17] Roth, A.E., The college admissions problem is not equivalent to the marriage problem, J. econ. theory, 36, 277-288, (1985) · Zbl 0594.90002
[18] Roth, A.E., On the allocation of residents to rural hospitalsa general property of two-sided matching markets, Econometrica, 54, 425-427, (1986)
[19] Roth, A.E., New physiciansa natural experiment in market organization, Science, 250, 1524-1528, (1990)
[20] Roth, A.E., A natural experiment in the organization of entry-level labor marketsregional markets for new physicians and surgeons in the united kingdom, Amer. econ. rev., 81, 415-440, (1991)
[21] Roth, A.E.; Sotomayor, M.A.O., Two-sided matching: A study in game-theoretic modeling and analysis, econometric society monograph series, (1990), Cambridge University Press New York
[22] Roth, A.E.; Xing, X., Jumping the gunimperfections and institutions related to the timing of market transactions, Amer. econ. rev., 84, 992-1044, (1994)
[23] Zhou, L., A new bargaining set of an N-person game and endogenous coalition formation, Games econ. behav., 6, 512-526, (1994) · Zbl 0807.90143
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