Seminar in Economic Theory:
Applications of Matching Markets
A matching market assigns objects to individuals, or individuals to each other. Typically, the different objects are indivisible and individuals differ in how much they value each of them, so that the assignment has important im- plications for the well-being of the individuals. Moreover, relevant applications involve markets where the use of monetary payments is limited or infeasible, such as public school choice, assignment of graduate students, or the exchange of live-donor kidneys for transplantation. In these markets, exhausting all op- portunities for mutually beneficial exchange with the limited means available is important for the well-being, and in the case of the last example, the health of those involved. This seminar will demonstrate how economic theory can offer some guidance for the design of markets in order to solve such problems of assignment.
Topics
The following presents a tentative list of topics and reading material. Topics marked with a single asterisk (*) require a lower formal background for under- standing than those marked (**). Some topics could potentially be shared by two students. Retrieving the papers on the reading list is part of the seminar;
forthcoming papers usually can be found as working papers on the authors’
webpages (which is always a good place to start looking).
Gale-Shapley and the Marriage Market
1. (*) Gale, D. and L. S. Shapley: 1962, ‘College Admissions and the Sta- bility of Marriage’. American Mathematical Monthly 69(3), 9–15.
2. (**) Becker, G. S.: 1973, ‘A Theory of Marriage: Part I’. The Journal of Political Economy 81(4), 813–846.
3. (*) Hitsch, G., Horta¸csu, A., and D. Ariely: 2009, ‘Matching and Sorting in Online Dating’. American Economic Review (forthcoming).
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Gale-Shapley on the Market for Medical Interns
4. (*) Dubins, L. E. and D. A. Freedman: 1981, ‘Machiavelli and the Gale- Shapley Algorithm’. American Mathematical Monthly 88(7), 485–494.
5. (*) Roth, A. E.: 1984, ‘The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory’. Journal of Political Economy 92(6), 991–1016., and (*) Roth, A. E.: 1986, ‘On the Allocation of Residents to Rural Hospitals: A General Property of Two- sided Matching Markets’. Econometrica 54(2), 425–427.
6. (*) Roth, A. E.: 1991, ‘A Natural Experiment in the Organization of Entry Level Labor Markets: Regional Markets for New Physicians and Surgeons in the United Kingdom’. American Economic Review 81(3), 415–440.
7. (**) Roth, A. E. and E. Peranson: 1999, ‘The Redesign of the Matching Market for American Physicians’. American Economic Review 89(4), 748–780.
School Choice
8. (**) Ergin, H. and T. S¨onmez: 2006, ‘Games of School Choice under the Boston Mechanism’. Journal of Public Economics90, 215–237.
9. (**) Abdulkadiroglu, A. and T. S¨onmez: 2003, ‘School Choice: A Mecha- nism Design Approach’. American Economic Review93(3), 729–747 and (*) Abdulkadiroglu, A., P. Pathak, A. E. Roth, and T. S¨onmez: 2005,
‘The Boston Public School Match’. American Economic Review Papers and Proceedings 95(2), 368–371.
10. (*) Abdulkadiroglu, A., P. Pathak, and A. E. Roth: 2005, ‘The New York City High School Match’. American Economic Review Papers and Pro- ceedings 95(2), 364-367 and Abdulkadiroglu, A., P. Pathak, and A. E.
Roth: 2005, ‘Strategy-proofness versus Efficiency in Matching with Indif- ferences: Redesigning the NYC High School Match. American Economic Review (forthcoming).
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Housing Markets
11. (**) Shapley, L. S. and M. Shubik: 1971, ‘The Assignment Game I: The Core’. International Journal of Game Theory1(1), 111–130.
12. (**) Shapley, L. S. and H. Scarf: 1974, ‘On Cores and Indivisibility’.
Journal of Mathematical Economics 1(1), 23–37.
13. (**) Abdulkadiroglu, A. and T. S¨onmez: 1999, ‘House Allocation with Existing Tenants’. Journal of Economic Theory 88(2), 233–260.
Kidney Exchange
14. (**) Roth, A. E., T. S¨onmez, and U. ¨Unver: 2004, ‘Kidney Exchange’.
Quarterly Journal of Economics 119(2), 457–488 and (*) Roth, A. E., T. S¨onmez, and U. ¨Unver: 2005a, ‘A Kidney Exchange Clearinghouse in New England’. American Economic Review Papers and Proceedings 95(2), 376–380.
15. (**) Roth, A. E., T. S¨onmez, and U. ¨Unver: 2005, ‘Pairwise Kidney Exchange’. Journal of Economic Theory 125(2), 151–188.
Auctions
16. (**) Demange, G., D. Gale, and M. Sotomayor: 1986, ‘Multi-item Auc- tions’. Journal of Political Economy94(4), 863–872.
17. (**) Kelso, A. S. and V. P. Crawford: 1982, ‘Job Matching, Coalition Formation, and Gross Substitutes’. Econometrica 50(6), 1483–1504.
18. (*) Milgrom, P.: 2000, ‘Putting auction Theory to Work: The Simultane- ous Ascending Auction’. Journal of Political Economy 108(2), 245–272.
Further Reading
For interesting background reading see for instance the survey by Niederle, M., Roth, A. E., and T. S¨onmez (2008, ‘Matching and Market Design’ in S. N. Durlauf and L. E. Blume (Eds.), New Palgrave Dictionary of Economics, 2nd Edition. Palgrave Macmillan) and the textbook by Roth, A. E. and M.
Sotomayor (1990, ‘Two-sided Matching: A Study in Game-Theoretic Modeling and Analysis’. Cambridge University Press).
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