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Random matching in the college admissions problem

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  • Joana Pais

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Abstract

In the college admissions problem, we consider the incentives confronting agents who face the prospect of being matched by a random stable mechanism. We provide a fairly complete characterization of ordinal equilbria. Namely, every ordinal equilib- rium yields a degenerate probability distribution. Furthermore, individual rationality is a necessary and sufficient condition for an equilibrium outcome, while stability is guaranteed in ordinal equilibrium where firms act straightforwardly. Finally, we re- late equilibrium behavior in random and in deterministic mechanisms.

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File URL: http://hdl.handle.net/10.1007/s00199-006-0191-6
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Bibliographic Info

Article provided by Springer in its journal Economic Theory.

Volume (Year): 35 (2008)
Issue (Month): 1 (April)
Pages: 99-116

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Handle: RePEc:spr:joecth:v:35:y:2008:i:1:p:99-116

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Web page: http://link.springer.de/link/service/journals/00199/index.htm

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Related research

Keywords: C78; Matching; College admissions problem; Stability; Random mechanism;

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References

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  1. Dipjyoti Majumdar, 2003. "Ordinally Bayesian Incentive Compatible Stable Matchings," Working Papers 05001, Concordia University, Department of Economics.
  2. Roth, Alvin E & Vande Vate, John H, 1990. "Random Paths to Stability in Two-Sided Matching," Econometrica, Econometric Society, vol. 58(6), pages 1475-80, November.
  3. Atila Abdulkadiroglu & Tayfun Smez, 2003. "School Choice: A Mechanism Design Approach," Discussion Papers 0203-18, Columbia University, Department of Economics.
  4. Roth, Alvin E., 1985. "The college admissions problem is not equivalent to the marriage problem," Journal of Economic Theory, Elsevier, vol. 36(2), pages 277-288, August.
  5. Roth, Alvin E. & Sotomayor, Marilda, 1992. "Two-sided matching," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 1, chapter 16, pages 485-541 Elsevier.
  6. d’ASPREMONT, C. & PELEG, B., 1986. "Ordinal Bayesian incentive compatible representations of committees," CORE Discussion Papers 1986042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  7. Joana Pais, 2006. "Incentives in Decentralized Random Matching Markets," Working Papers 2006/12, Department of Economics at the School of Economics and Management (ISEG), Technical University of Lisbon..
  8. Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116.
  9. Joana Pais, 2006. "On Random Matching Markets: Properties and Equilibria," Working Papers 2006/11, Department of Economics at the School of Economics and Management (ISEG), Technical University of Lisbon..
  10. Abdulkadiroglu, Atila & Sonmez, Tayfun, 1999. "House Allocation with Existing Tenants," Journal of Economic Theory, Elsevier, vol. 88(2), pages 233-260, October.
  11. Dipjyoti Majumdar & Arunava Sen, 2004. "Ordinally Bayesian Incentive Compatible Voting Rules," Econometrica, Econometric Society, vol. 72(2), pages 523-540, 03.
  12. Roth, Alvin E, 1984. "The Evolution of the Labor Market for Medical Interns and Residents: A Case Study in Game Theory," Journal of Political Economy, University of Chicago Press, vol. 92(6), pages 991-1016, December.
  13. Roth, Alvin E & Vande Vate, John H, 1991. "Incentives in Two-Sided Matching with Random Stable Mechanisms," Economic Theory, Springer, vol. 1(1), pages 31-44, January.
  14. Ehlers, Lars & Masso, Jordi, 2007. "Incomplete information and singleton cores in matching markets," Journal of Economic Theory, Elsevier, vol. 136(1), pages 587-600, September.
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Citations

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Cited by:
  1. Pais, Joana, 2008. "Incentives in decentralized random matching markets," Games and Economic Behavior, Elsevier, vol. 64(2), pages 632-649, November.
  2. Horstschräer, Julia, 2012. "Decentralizing university admission: Evidence from a natural experiment," ZEW Discussion Papers 12-076, ZEW - Zentrum für Europäische Wirtschaftsforschung / Center for European Economic Research.
  3. Haeringer, Guillaume & Klijn, Flip, 2009. "Constrained school choice," Journal of Economic Theory, Elsevier, vol. 144(5), pages 1921-1947, September.
  4. Christoph Müller, 2009. "Wie lässt sich die Zulassungsinformation der Studieninteressenten verbessern?," Journal of Economics and Statistics (Jahrbuecher fuer Nationaloekonomie und Statistik), Justus-Liebig University Giessen, Department of Statistics and Economics, vol. 229(5), pages 544-569, October.

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