Equilibria under Deferred Acceptance: Dropping Strategies, Filled Positions, and Welfare
This 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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| Length: | 20 |
| Date of creation: | 10 Apr 2013 |
| Date of revision: | |
| Handle: | RePEc:col:000089:010737 |
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- Roth, Alvin E & Sotomayor, Marilda, 1989. "The College Admissions Problem Revisited," Econometrica, Econometric Society, vol. 57(3), pages 559-70, May.
- Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
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- Roth, Alvin, 2008. "Deferred Acceptance Algorithms: History, Theory, Practice, and Open Questions," Scholarly Articles 2579651, Harvard University Department of Economics.
- Sonmez, Tayfun, 1997. "Manipulation via Capacities in Two-Sided Matching Markets," Journal of Economic Theory, Elsevier, vol. 77(1), pages 197-204, November.
- Paula Jaramillo & Cagatay Kay & Flip Klijn, 2012.
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DOCUMENTOS CEDE
010316, UNIVERSIDAD DE LOS ANDES-CEDE.
- Paula Jaramillo & Çaǧatay Kayı & Flip Klijn, 2014. "On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 42(4), pages 793-811, April.
- Paula Jaramillo & Kagi Cagatay & Flip Klijn, 2012. "On the exhaustiveness of truncation and dropping strategies in many-to-many matching markets," DOCUMENTOS DE TRABAJO 009997, UNIVERSIDAD DEL ROSARIO.
- Paula Jaramillo & Ça?atay Kay? & Flip Klijn, 2012. "On the Exhaustiveness of Truncation and Dropping Strategies in Many-to-Many Matching Markets," Working Papers 632, Barcelona Graduate School of Economics.
- Klijn, Flip & Yazıcı, Ayşe, 2014.
"A many-to-many ‘rural hospital theorem’,"
Journal of Mathematical Economics,
Elsevier, vol. 54(C), pages 63-73.
- Flip Klijn & Ayse Yazici, 2014. "A Many-to-Many "Rural Hospital Theorem"," Working Papers 567, Barcelona Graduate School of Economics.
- Flip Klijn, 2011. "A Many-to-Many 'Rural Hospital Theorem'," UFAE and IAE Working Papers 877.11, Unitat de Fonaments de l'Anàlisi Econòmica (UAB) and Institut d'Anàlisi Econòmica (CSIC).
- Marilda Sotomayor, 2008. "The stability of the equilibrium outcomes in the admission games induced by stable matching rules," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 621-640, March.
- Blum, Yosef & Roth, Alvin E. & Rothblum, Uriel G., 1997. "Vacancy Chains and Equilibration in Senior-Level Labor Markets," Journal of Economic Theory, Elsevier, vol. 76(2), pages 362-411, October.
- Sotomayor, Marilda, 1996. "A Non-constructive Elementary Proof of the Existence of Stable Marriages," Games and Economic Behavior, Elsevier, vol. 13(1), pages 135-137, March.
- Roth, Alvin E & Vande Vate, John H, 1991. "Incentives in Two-Sided Matching with Random Stable Mechanisms," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 1(1), pages 31-44, January.
- Roth, Alvin E, 1986. "On the Allocation of Residents to Rural Hospitals: A General Property of Two-Sided Matching Markets," Econometrica, Econometric Society, vol. 54(2), pages 425-27, March.
- Fuhito Kojima & Parag A. Pathak, 2009. "Incentives and Stability in Large Two-Sided Matching Markets," American Economic Review, American Economic Association, vol. 99(3), pages 608-27, June.
- Marilda Sotomayor, 2012. "A further note on the college admission game," International Journal of Game Theory, Springer;Game Theory Society, vol. 41(1), pages 179-193, February.
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