Variations of the Gale-Shapley algorithm have been used and studied extensively in real world markets. Examples include matching medical residents with residency programs, the kidney exchange program and matching college students with on-campus housing. The performance of the Gale-Shapley marriage matching algorithm (1962) has been studied extensively in the special case of men's and women's preferences random. We drop the assumption that women's preferences are random and show that En /n ln n -> 1, where En is the expected number of proposals made when the men-propose Gale-Shapley algorithm is used to match n men with n women. This establishes in spirit a conjecture of Donald Knuth (1976, 1997) of thirty years standing. Under the same assumptions, we also establish bounds on the expected ranking by a woman of her assigned mate. Bounds on men's rankings of their assigned mates follow directly from the conjecture.
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Paper provided by University of Connecticut, Department of Economics in its series Working papers with number
2007-15.
Length: 16 pages Date of creation: May 2007 Date of revision: Handle: RePEc:uct:uconnp:2007-15
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Find related papers by JEL classification: C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory D63 - Microeconomics - - Welfare Economics - - - Equity, Justice, Inequality, and Other Normative Criteria and Measurement D70 - Microeconomics - - Analysis of Collective Decision-Making - - - General
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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.:
Alvin E. Roth & Tayfun Sönmez & M. Utku Ünver, 2004.
"Kidney Exchange,"
The Quarterly Journal of Economics,
MIT Press, vol. 119(2), pages 457-488, May.
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Alvin E. Roth & Tayfun Sonmez & M. Utku Unver, 2003.
"Kidney Exchange,"
NBER Working Papers
10002, National Bureau of Economic Research, Inc.
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