On the existence of a strictly strong Nash equilibrium under the student-optimal deferred acceptance algorithm |
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Affiliation: | 1. Department of Government, University of Essex, Wivenhoe Park, Colchester CO4 3SQ, United Kingdom;2. Faculty of Engineering, Information and Systems, University of Tsukuba, 1-1-1 Tennodai, Tsukuba, Ibaraki 305-8573, Japan;3. WZB Berlin Social Science Center, Reichpietschufer 50, D-10785 Berlin, Germany;4. Department of Economics, University of Heidelberg, Bergheimer Str. 58, 69115 Heidelberg, Germany;1. Faculty of Economics, Kansai University, 3-3-35, Yamate-cho, Suita-shi, Osaka 564-8680, Japan;2. Faculty of Economics, Ryukoku University, 67 Tsukamoto-cho, Fukakusa, Fushimi-ku, Kyoto 612-8577, Japan;1. eBay Data Labs, United States;2. Harvard University, United States;3. Harvard Business School, United States |
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Abstract: | This study analyzes a preference revelation game in the student-optimal deferred acceptance algorithm in a college admission problem. We assume that each college's true preferences are known publicly, and analyze the strategic behavior of students. We demonstrate the existence of a strictly strong Nash equilibrium in the preference revelation game through a simple algorithm that finds it. Specifically, (i) the equilibrium outcome from our algorithm is the same matching as in the efficiency-adjusted deferred acceptance algorithm and (ii) in a one-to-one matching market, it coincides with the student-optimal von Neumann–Morgenstern (vNM) stable matching. We also show that (i) when a strict core allocation in a housing market derived from a college admission market exists, it can be supported by a strictly strong Nash equilibrium, and (ii) there exists a strictly strong Nash equilibrium under the college-optimal deferred acceptance algorithm if and only if the student-optimal stable matching is Pareto-efficient for students. |
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Keywords: | Student-optimal deferred acceptance algorithm Strictly strong Nash equilibrium Efficiency-adjusted deferred acceptance algorithm Student-optimal vNM stable matching |
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