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).
|Date of creation:||10 Apr 2013|
|Contact details of provider:|| |
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Alvin E Roth, 2007.
"Deferred Acceptance Algorithms: History, Theory, Practice, and Open Questions,"
843644000000000283, UCLA Department of Economics.
- Roth, Alvin, 2008. "Deferred Acceptance Algorithms: History, Theory, Practice, and Open Questions," Scholarly Articles 2579651, Harvard University Department of Economics.
- Alvin E. Roth, 2007. "Deferred Acceptance Algorithms: History, Theory, Practice, and Open Questions," NBER Working Papers 13225, National Bureau of Economic Research, Inc.
- Alvin Roth, 2008. "Deferred acceptance algorithms: history, theory, practice, and open questions," International Journal of Game Theory, Springer;Game Theory Society, vol. 36(3), pages 537-569, March.
- 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, 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).
- Flip Klijn & Ayse Yazici, 2014. "A Many-to-Many "Rural Hospital Theorem"," Working Papers 567, Barcelona Graduate School of Economics.
- Roth, Alvin E & Sotomayor, Marilda, 1989. "The College Admissions Problem Revisited," Econometrica, Econometric Society, vol. 57(3), pages 559-570, May.
- Paula Jaramillo & Cagatay Kay & Flip Klijn, 2012.
"On the Exhaustiveness of Truncation and Dropping Strategies in Many-to-Many Matching Markets,"
010316, UNIVERSIDAD DE LOS ANDES-CEDE.
- 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.
- 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.
- 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.
- 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.
- Roth, Alvin E., 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Scholarly Articles 29410143, 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.
- 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 425-427, 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 608-627, June.
- 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.
- 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.
When requesting a correction, please mention this item's handle: RePEc:col:000089:010737. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Universidad De Los Andes-Cede)
If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.
If references are entirely missing, you can add them using this form.
If the full references list an item that is present in RePEc, but the system did not link to it, you can help with this form.
If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your profile, as there may be some citations waiting for confirmation.
Please note that corrections may take a couple of weeks to filter through the various RePEc services.