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Stable matchings and the small core in Nash equilibrium in the college admissions problem. (English) Zbl 1055.91003

This paper studies the problem of misrepresentation in a class of stable matching mechanisms in the college admissions problem (including marriage as a special case). The paper shows that in such a problem, although examples exist in which rematching-proof or strong equilibrium outcomes are unstable with respect to true preferences, rematching-proof or strong equilibrium outcomes in truncations at the match point are stable, and all stable matchings can be supported by both rematching-proof and strong equilibrium in truncations at the match point. The paper also shows that every Nash equilibrium profile admits at most one true stable matching.

MSC:

91A12 Cooperative games
91B68 Matching models
91A10 Noncooperative games
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