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College Admissions

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  • M. Bumin Yenmez

Abstract

I propose a centralized clearinghouse for college admissions in which students can signal enthusiasm by commitment, like early-decision programs. Furthermore, students can specify financial aid in their preferences and they can be matched with multiple colleges at the same time. This clearinghouse keeps the desirable properties of the decentralized college admissions like signalling and yield management while getting rid of the undesirable aspects such as unfairness and unraveling. To study centralized college admissions, I advance the theory of stability for many-to-many matching markets with contracts. In particular, I show that stable matchings exist even when colleges do not have path-independent (or substitutable) choice rules. I provide two results on comparative statics for the student-proposing deferred acceptance algorithm. Furthermore, I introduce a new monotonicity condition on choice rules to study yield management for colleges and generalize the rural-hospitals theorem when contracts may have different weights. My framework opens new venues for market-design research and raises questions about the standard assumptions made in the literature.

Suggested Citation

  • M. Bumin Yenmez, 2014. "College Admissions," GSIA Working Papers 2014-E24, Carnegie Mellon University, Tepper School of Business.
    • Handle: RePEc:cmu:gsiawp:-1287045339
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    File URL: https://student-3k.tepper.cmu.edu/gsiadoc/WP/2014-E24.pdf
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    References listed on IDEAS

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    1. Echenique, Federico, 2007. "Counting combinatorial choice rules," Games and Economic Behavior, Elsevier, vol. 58(2), pages 231-245, February.
    2. Christopher P. Chambers & M. Bumin Yenmez, 2017. "Choice and Matching," American Economic Journal: Microeconomics, American Economic Association, vol. 9(3), pages 126-147, August.
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    7. Christopher Avery & Jonathan Levin, 2010. "Early Admissions at Selective Colleges," American Economic Review, American Economic Association, vol. 100(5), pages 2125-2156, December.
    8. Tayfun Sönmez, 2013. "Bidding for Army Career Specialties: Improving the ROTC Branching Mechanism," Journal of Political Economy, University of Chicago Press, vol. 121(1), pages 186-219.
    9. Michael Ostrovsky, 2008. "Stability in Supply Chain Networks," American Economic Review, American Economic Association, vol. 98(3), pages 897-923, June.
    10. Hatfield, John William & Kojima, Fuhito, 2010. "Substitutes and stability for matching with contracts," Journal of Economic Theory, Elsevier, vol. 145(5), pages 1704-1723, September.
    11. Tamás Fleiner, 2003. "A Fixed-Point Approach to Stable Matchings and Some Applications," Mathematics of Operations Research, INFORMS, vol. 28(1), pages 103-126, February.
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    13. Pycia, Marek & Yenmez, M. Bumin, 2019. "Matching with Externalities," CEPR Discussion Papers 13994, C.E.P.R. Discussion Papers.
    14. Orhan Aygün & Tayfun Sönmez, 2012. "The Importance of Irrelevance of Rejected Contracts in Matching under Weakened Substitutes Conditions," Boston College Working Papers in Economics 805, Boston College Department of Economics.
    15. Roth, Alvin E, 1984. "Stability and Polarization of Interests in Job Matching," Econometrica, Econometric Society, vol. 52(1), pages 47-57, January.
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    20. Balinski, Michel & Sonmez, Tayfun, 1999. "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory, Elsevier, vol. 84(1), pages 73-94, January.
    21. M. Bumin Yenmez, 2013. "Incentive-Compatible Matching Mechanisms: Consistency with Various Stability Notions," American Economic Journal: Microeconomics, American Economic Association, vol. 5(4), pages 120-141, November.
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    Cited by:

    1. Antonio Romero-Medina & Matteo Triossi, 2023. "Take-it-or-leave-it contracts in many-to-many matching markets," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 75(2), pages 591-623, February.
    2. Hafalir, Isa E. & Hakimov, Rustamdjan & Kübler, Dorothea & Kurino, Morimitsu, 2018. "College admissions with entrance exams: Centralized versus decentralized," EconStor Open Access Articles and Book Chapters, ZBW - Leibniz Information Centre for Economics, vol. 176, pages 886-934.
    3. Hatfield, John William & Kominers, Scott Duke, 2017. "Contract design and stability in many-to-many matching," Games and Economic Behavior, Elsevier, vol. 101(C), pages 78-97.
    4. Scott Duke Kominers & Tayfun Sönmez, 2012. "Designing for Diversity: Matching with Slot-Specific Priorities," Boston College Working Papers in Economics 806, Boston College Department of Economics.

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