The singleton core in the college admissions problem and its application to the National Resident Matching Program (NRMP)

Jinpeng Ma ()

Games and Economic Behavior, 2010, vol. 69, issue 1, 150-164

Abstract: We show that in the marriage problem the student-optimal algorithm may in fact generate an equilibrium outcome that is college-optimal and student-pessimal in terms of the true preferences even though it is student-optimal and college-pessimal in terms of the submitted preferences. In the college admissions problem, the student-optimal algorithm generates either a matching that is not stable for the true preferences or a matching that is college-optimal and student-pessimal in terms of the true preferences. Thus, our results show that, in the absence of certain match variations, the newly designed student-optimal algorithm adopted by the NRMP since 1998 either may be bias in favor of hospitals in terms of the true preferences or fails to produce a true stable matching. We also discuss when the core is large and when the core is a singleton at a Nash equilibrium.

Date: 2010
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