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The college admissions problem is not equivalent to the marriage problem.(English)Zbl 0594.90002

Summary: Two-sided matching markets of the kind known as the “college admissions problem” have been widely thought to be virtually equivalent to the simpler “marriage problem” for which some striking results concerning agents’ preferences and incentives have been recently obtained. It is shown here that some of these results do not generalize to the college admissions problem, contrary to a number of assertions in the recent literature. No stable matching procedure exists that makes it a dominant strategy for colleges to reveal their true preferences, and some outcomes may be preferred by all colleges to the college-optimal stable outcome.

MSC:

91B68 Matching models
91B08 Individual preferences

Cite

References:

[1]Dubins, L. E.; Freedman, D. A., Machiavelli and the Gale-Shapley algorithm, Amer. Math. Montly, 88, 485-494 (1981) ·Zbl 0449.92024
[2]Gale, D., Ms. Machiavelli and the Gale-Shapley algorithm (1983), mimeo
[3]Gale, D.; Shapley, L., College admissions and the stability of marriage, Amer. Math. Monthly, 69, 9-15 (1962) ·Zbl 0109.24403
[4]Gale, D.; Sotomayor, M., Some remarks on the stable matching problem (1983), mimeo
[5]Kelso, A. S.; Crawford, V. P., Job matching, coalition formation, and gross substitutes, Econometrica, 50, 1483-1504 (1982) ·Zbl 0503.90019
[6]Roth, A. E., The economics of matching: Stability and incentives, Math. Oper. Res., 7, 617-628 (1982) ·Zbl 0496.90008
[7]Roth, A. E., Misrepresentation and stability in the marriage problem, J. Econ. Theory, 34, 383-387 (1984) ·Zbl 0549.90006
[8]Roth, A. E., Stability and polarization of interests in job matching, Econometrica, 52, 47-57 (1984) ·Zbl 0526.90012
[9]Roth, A. E., The evolution of the labor market for medical interns and residents: A case study in game theory, J. Polit. Econ., 92, 991-1016 (1984)
[10]Roth, A. E., Common and conflicting interests in two-sided matching markets, European Economic Review (1985), forthcoming
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.
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