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Some things couples always wanted to know about stable matchings (but were afraid to ask). (English) Zbl 1136.91542
Summary: In this note we study the National Resident Matching Program (NRMP) algorithm in the US market for physicians. We report on two problems that concern the presence of couples, a feature explicitly incorporated in the new NRMP algorithm [cf. A. E. Roth and E. Peranson, The redesign of the matching market for American physicians: some engineering aspects of economic design. Am. Econ. Rev. 89, 748–780 (1999)]. First, we show that the new NRMP algorithm may not find an existing stable matching, even when couples’ preferences are ‘responsive’, i.e., when D. Gale and L. S. Shapley [Am. Math. Mon. 69, 9–15 (1962; Zbl 0109.24403)] deferred acceptance algorithm (on which the old NRMP algorithm is based) is applicable. Second, we demonstrate that the new NRMP algorithm may also be anipulated by couples acting as singles.

MSC:
91B68 Matching models
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