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College Admissions under Early Decision

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Author Info
Mumcu, Ayse
Saglam, Ismail

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Abstract

In this paper, we model college admissions under early decision in a many-to-one matching framework with two periods. We show that there exists no stable matching system, involving an early decision matching rule and a regular decision matching rule, which is nonmanipulable via early decision quotas by colleges or via early decision preferences by colleges or students. We then analyze the Nash equilibria of the game, in which the preferences of colleges and students in each period are common knowledge and every college determines a quota for the early decision period given its total capacity for the two periods. Under college-optimal and student-optimal matching systems, we show that a pure strategy equilibrium may not exist. However, when colleges or students have common preferences over the other set of agents, 'terminating early decision program' becomes a weakly dominant strategy for each college if every student, choosing to act early, always applies early to his or her top choice college.

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Publisher Info
Paper provided by University Library of Munich, Germany in its series MPRA Paper with number 1906.

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Date of creation: 25 Jan 2007
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Handle: RePEc:pra:mprapa:1906

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Related research
Keywords: Many-to-one matching; college admissions; early decision;

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Find related papers by JEL classification:
C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games
C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory

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References listed on IDEAS
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  1. Szilvia Papai, 2000. "Strategyproof Assignment by Hierarchical Exchange," Econometrica, Econometric Society, vol. 68(6), pages 1403-1434, November.
  2. Caroline M. Hoxby, 2000. "Benevolent Colluders? The Effects of Antitrust Action on College Financial Aid and Tuition," NBER Working Papers 7754, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  3. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August. [Downloadable!] (restricted)
  4. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541 Elsevier. [Downloadable!] (restricted)
  5. Sonmez, Tayfun, 1999. "Can Pre-arranged Matches Be Avoided in Two-Sided Matching Markets?," Journal of Economic Theory, Elsevier, vol. 86(1), pages 148-156, May. [Downloadable!] (restricted)
  6. Sonmez, Tayfun, 1997. "Manipulation via Capacities in Two-Sided Matching Markets," Journal of Economic Theory, Elsevier, vol. 77(1), pages 197-204, November. [Downloadable!] (restricted)
  7. Atila Abdulkadiroglu & Tayfun Sonmez, 1998. "Random Serial Dictatorship and the Core from Random Endowments in House Allocation Problems," Econometrica, Econometric Society, vol. 66(3), pages 689-702, May.
  8. Mongell, Susan & Roth, Alvin E, 1991. "Sorority Rush as a Two-Sided Matching Mechanism," American Economic Review, American Economic Association, vol. 81(3), pages 441-64, June. [Downloadable!] (restricted)
  9. Roth, Alvin E & Xing, Xiaolin, 1994. "Jumping the Gun: Imperfections and Institutions Related to the Timing of Market Transactions," American Economic Review, American Economic Association, vol. 84(4), pages 992-1044, September. [Downloadable!] (restricted)
  10. Hideo Konishi & M. Ünver, 2006. "Games of Capacity Manipulation in Hospital-intern Markets," Social Choice and Welfare, Springer, vol. 27(1), pages 3-24, August. [Downloadable!] (restricted)
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  11. Christopher Avery & Mark Glickman & Caroline Hoxby & Andrew Metrick, 2004. "A Revealed Preference Ranking of U.S. Colleges and Universities," NBER Working Papers 10803, National Bureau of Economic Research, Inc. [Downloadable!] (restricted)
  12. Alvin E. Roth & Uriel G. Rothblum, 1999. "Truncation Strategies in Matching Markets--In Search of Advice for Participants," Econometrica, Econometric Society, vol. 67(1), pages 21-44, January.
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