Equilibria under Deferred Acceptance: Dropping Strategies, Filled Positions, and Welfare
AbstractThis paper studies many-to-one matching markets where each student is assigned to a hospital. Each hospital has possibly multiple positions and responsive preferences. We study the game induced by the student-optimal stable matching mechanism. We assume that students play their weakly dominant strategy of truth-telling. Roth and Sotomayor (1990) showed that there can be unstable equilibrium outcomes. We prove that any stable matching can be obtained in some equilibrium. We also show that the exhaustive class of dropping strategies does not necessarily generate the full set of equilibrium outcomes. Finally, we find that the so-called ‘rural hospital theorem' cannot be extended to the set of equilibrium outcomes and that welfare levels are in general unrelated to the set of stable matchings. Two important consequences are that, contrary to one-to-one matching markets, (a) filled positions depend on the particular equilibrium that is reached and (b) welfare levels are not bounded by the student and hospital-optimal stable matchings (with respect to the true preferences).
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Bibliographic InfoPaper provided by UNIVERSIDAD DE LOS ANDES-CEDE in its series DOCUMENTOS CEDE with number 010737.
Date of creation: 10 Apr 2013
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- Jaramillo, Paula & Kayı, Çaǧatay & Klijn, Flip, 2013. "Equilibria under deferred acceptance: Dropping strategies, filled positions, and welfare," Games and Economic Behavior, Elsevier, vol. 82(C), pages 693-701.
- Paula Jaramillo & Çagatay Kayi & Flip Klijn, 2013. "Equilibria under Deferred Acceptance: Dropping Strategies, Filled Positions, and Welfare," Working Papers 686, Barcelona Graduate School of Economics.
- C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
- D60 - Microeconomics - - Welfare Economics - - - General
This paper has been announced in the following NEP Reports:
- NEP-ALL-2013-05-22 (All new papers)
- NEP-GTH-2013-05-22 (Game Theory)
- NEP-MIC-2013-05-22 (Microeconomics)
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