Abstract
When a stable matching rule is used for a college admission market, questions on incentives facing agents of both sides of the market naturally emerge. This note states and proves four important results which fill a gap in the theory of incentives for the college admission model. Two of them have never been demonstrated but have been used along the years and are responsible for the success that this theory has had in explaining empirical economic phenomena.
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References
Alcalde (1996) Implementation of stable solutions to marriage problems. J Econ Theory 69: 240–254
Dubins LE, Freedman DA (1981) Machiavelli and the Gale–Shapley algorithm. Am Math Mon 88: 485–494
Gale D, Sotomayor M (1983/1985a) Some remarks on the stable matching problem. Discret Appl Math 11:223–232
Gale D, Sotomayor M (1983/1985b) Ms. Machiavelli and the stable matching problem. Am Math Mon 92:261–268
Haeringer G, Klijn F (2009) Constrained school choice. J Econ Theory 144: 1921–1947
Hatfield JW, Milgrom P (2005) Matching with contracts. Am Econ Rev 95(4): 913–935
Kalai E, Postlewaite A, Roberts J (1979) A group incentive compatible mechanism yielding core allocations. J Econ Theory 20: 13–22
Kelso AS Jr, Crawford VP (1982) Job matching, coalition formation, and gross substitutes. Econometrica 50: 1483–1504
Kojima F, Pathak P (2009) Incentives and stability in large two-sided matching markets. Am Econ Rev 99(3): 608–627
Konishi H, Unver U (2006) Games of capacity manipulation in hospital-intern markets. Soc Choice Welf 27: 3–24
Ma J (2002) Stable matchings and the small core in Nash equilibrium in the College Admission Problem. Rev Econ Des 7: 117–134
Roth A (1984) Misrepresentation and stability in the marriage problem. J Econ Theory 34: 383–387
Roth A (1985) The college admissions problem is not equivalent to the marriage problem. J Econ Theory 36: 277–288
Roth A (1986) On the allocation of residents to rural hospitals: a general property of two-sided matching markets. Econometrica 54: 425–427
Roth A, Sotomayor M (1989) The college admissions problem revisited. Econometrica 57: 559–570
Roth A, Sotomayor M (1990) Two-sided matching. A study in game-theoretic modeling and analysis. Econometric society monographs No. 18, Cambridge
Sönmez T (1997a) Games of manipulation in marriage problems. Games Econ Behav 20: 169–176
Sönmez T (1997b) Manipulation via capacities in two-sided matching markets. J Econ Theory 77: 197–204
Sotomayor M (1996) Admission mechanisms of students to colleges. A game-theoretic modeling and analysis. Braz Rev Econ 16(1): 25–63
Sotomayor M (1998) The strategy structure of the college admissions stable mechanisms”, mimeo. (Annals of Jornadas Latino Americanas de Teoria Economica, San Luis, Argentina (2000), First World Congress of the Game Theory Society (Bilbao, 2000), 4rth Spanish Meeting Valencia 2000), International Symposium of Mathematical Programming (Atlanta, 2000), World Congress of the Econometric Society (Seattle, 2000)
Sotomayor M (2001) Implementation in the many-to-many matching market. Games Econ Behav 46: 199–212
Sotomayor M (2003) Reaching the core of the marriage market through a non-revelation matching mechanism. Int J Game Theory 32: 241–251
Sotomayor M (2008) The stability of the equilibrium outcomes in the admission games induced by stable matching rules. Int J Game Theory (Special issue in honor of David Gale, Edit. by M. Sotomayor) 36: 621–640
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Sotomayor, M. A further note on the college admission game. Int J Game Theory 41, 179–193 (2012). https://doi.org/10.1007/s00182-011-0278-6
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DOI: https://doi.org/10.1007/s00182-011-0278-6