Singleton core in many-to-one matching problems |
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| Institution: | 1. Department of Economics, Seoul National University, Seoul, South Korea;2. Economic Research Unit, Indian Statistical Institute, Kolkata, India;3. Department of Economics, University of Leicester, Leicester, United Kingdom;1. Facultad de Economía y Empresa, Universidad de Salamanca, E 37008, Salamanca, Spain;2. Department of Economics and Finance, School of Business, Montclair State University, Montclair, NJ 07043, USA;1. CER—ETH Center of Economic Research, ETH Zurich, Switzerland;2. CentER and Department of Econometrics and Operations Research, Tilburg University, Netherlands;3. Quintiq Inc., United States;1. Baruch College, United States of America;2. Normandie Université, UNIROUEN, CREAM, France;1. School of Sciences, China University of Mining and Technology, Xuzhou, 221116, PR China;2. Belk College of Business, University of North Carolina at Charlotte, Charlotte, NC, 28223, USA |
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| Abstract: | We explore two necessary and sufficient conditions for the singleton core in college admissions problems. One is a condition on the colleges’ preference profiles, called acyclicity, and the other is a condition on their capacity vectors. We also study the implications of our acyclicity condition. The student-optimal stable matching is strongly efficient for the students, given an acyclic profile of the colleges’ preference relations. Even when the colleges’ true preference profile is acyclic, a college may be better off by misreporting its preference when the college-optimal stable mechanism is used. |
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