Mumcu, Ayse and Saglam, Ismail (2007): College Admissions under Early Decision.
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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.
|Item Type:||MPRA Paper|
|Original Title:||College Admissions under Early Decision|
|Keywords:||Many-to-one matching; college admissions; early decision|
|Subjects:||C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C71 - Cooperative Games
C - Mathematical and Quantitative Methods > C7 - Game Theory and Bargaining Theory > C78 - Bargaining Theory ; Matching Theory
|Depositing User:||Ayşe Mumcu|
|Date Deposited:||25. Feb 2007|
|Last Modified:||14. Feb 2013 01:57|
Abdulkadiroglu, A. and Sonmez, T. "Random Serial Dictatorship and the Core from Random Endowments in House Allocation Problems," Econometrica, 1998, 66(3), 689-701.
Avery, C., Fairbanks, A. and Zeckhauser, R. The Early Admissions Game:Joining the Elite. Cambridge: Harvard University Press, 2003.
Avery, C., Glickman, M., Metrick, A. and Hoxby, C.M. "A Revealed Preference Ranking of American Colleges and Universities", NBER Working Paper 10803, 2004.
Gale, D. and Shapley, L.S. "College Admissions and the Stability of Marriage," American Mathematical Monthly, 1962, 69(1), 9-15.
Hoxby, C.M. "Benevolent Colluders? The Effects of Antitrust Action on College Fianancial Aid and Tuition," NBER Working Paper 7754, 2000.
Konishi, H. and Unver, M.U. "Games of Capacity Manipulation in Hospital-Intern Markets," Social Choice and Welfare, 2006, 27(1), 3-24.
Mongell, S. and Roth, A.E. "Sorority Rush as a Two-Sided Matching Mechanism," American Economic Review, 1991, 81(3), 441-464.
Roth, A.E. "The Economics of Matching: Stability and Incentives," Mathematics of Operations Research, 1982, 7(4), 617-628.
Roth, A.E. "The College Admissions Problem is not Equivalent to the Marriage Problem," Journal of Economic Theory, 1985, 36(2), 277-288.
Roth, A.E. and Rothblum, U.G. "Truncation Strategies in Matching Markets in Search of Advice for Participants," Econometrica, 1999, 67(1),21-43.
Roth, A.E. and Sotomayor, M. Two-Sided Matching: A Study in Game Theoretic Modeling and Analysis. London/New York: Cambridge University Press, 1990.
Roth, A.E. and Vande Vate, J.H. "Incentives in Two-Sided Matching with Random Stable Mechanism," Economic Theory, 1991, 1(1), 31-44.
Roth, A.E. and Xing, X. "Jumping the Gun: Imperfections and Institutions Related to the Timing of Market Transactions,"American Economic Review}, 1994, 84(4), 992-1044.
Papai, S. "Strategyproof Assignment by Hierarchical Exchange," Econometrica}, 2000, 68(6), 1403-1433.
Sonmez, T. "Manipulation via Capacities in Two-Sided Matching Markets," Journal of Economic Theory, 1997, 77(1), 197-204.
Sonmez, T. "Can Pre-Arranged Matches Be Avoided in Two-Sided Matching Markets?," Journal of Economic Theory, 1999, 86(1), 148-156.
Svensson, L.G. "Queue Allocation of Indivisible Goods," Social Choice and Welfare}, 1994, 11(4), 323-330.