September 2014
New York University
Matching Theory Mini Course:
Primer and Some Recent Development
Yeon-Koo Che
Matching theory has taken a center stage in market design specifically and
economic theory more generally, with successful practical applications in
medical matching and school choice. The current course provides a basic
introduction into matching theory, discusses “school choice” as an application, and touches upon some frontier topics in matching theory research.
Specifically, we will discuss some basic theories of two-sided matching,
studying design objectives such as stability, efficiency, and incentives. We
will study how these objectives conflict each other in the finite markets
such as in the context of school choice, and then study whether and how
the conflicts get resolved in the large markets.
• General Information:
– Class Hours: Monday: 1:00-3:00PM, Sept 8, 15 and 22
– Location: Room 736.
– Contact Information: (E-mail) yeonkooche@gmail.com
– Office Hours: via email appointment.
Course Outline
Lecture 1 (Sept 8): Primer on Two-Sided Matching Theory
• Roth, A., and Sotomayor, M., Two-sided Matching: A Study in Game-theoretic
Modeling and Analysis, Econometric Society Monographs, 1990. Chapters, 2-5.
Lecture 2 (Sept 15): School Choice Application
• * Abdulkadiroglu, A., and Sonmez, T., 2003, ”School Choice: A Mechanism
Design Approach”, American Economic Review, 93-3: 729-747.
• Ergin, 2002, “Efficient Resource Allocation on the Basis of Priorities,” Econometrica.
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• Abdulkadiroğlu, A., Pathak, P., and Roth, E., 2006, “Strategy-proofness versus
Efficiency in Matching with Indifferences: Redesigning the NYC High School
Match,” American Economic Review, 99, 1954-78.
• Erdil, A., and Ergin, H., 2008, “What’s the Matter with Tie-breaking? Improving Efficiency with School Choice,” American Economic Review, 98, 669-689.
• *Abdulkadiroglu, A., Che, Y.-K., and Yasuda, Y., 2011, “Resolving Conflicting
Preferences in School Choice: The Boston Mechanism Recon- sidered,” American Economic Review.
• Abdulkadiroglu, A., Che, Y.-K., and Yasuda, Y., 2013, “Expanding Choice in
School Choice.” AEJ: Micro, forthcoming.
Lecture 3 (Sept 22): Large Matching Markets
• Roth, A., and Peranson, E. (1999), “The Redesign of the Matching Market for
American Physicians: Some Engineering Aspects of Economic Design,” American Economic Review, 89, 748-780.
• Pittel, B., (1992), “On Likely Solutions of a Stable Marriage Problem,” The
Annals of Applied Probability, 2, 358-401.
• Wilson, L.B., (1972), “An Analysis of the Stable Marriage Assignment Algorithm,” BIT 12, 569-575
• Kojima, F. and Pathak, P. A. (2009), Incentives and stability in large two-sided
matching markets. American Economic Review, 99, 608-627.
• Ashlagi, I., Kanoria, Y., and Leshno, J., (2014), “Unbalanced Random Matching
Markets: the Stark Effect of Competition,” mimeo, Columbia University.
• *Che, Y.-K., and Tercieux, O., “Efficiency and Stability in the Large Matching
Markets,” mimeo., Columbia University and PSE.
• *Che, Y.-K., Kim, J., and Kojima, F., “Stable Matching in Large Economies,”
mimeo., Columbia University and PSE.
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