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Random Matching in the College Admissions Problem

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  • Joana Pais

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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Bibliographic Info

Paper provided by ISEG - School of Economics and Management, Department of Economics, University of Lisbon in its series Working Papers Department of Economics with number 2006/13.

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Date of creation: 2006
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Handle: RePEc:ise:isegwp:wp132006

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Postal: Department of Economics, ISEG - School of Economics and Management, University of Lisbon, Rua do Quelhas 6, 1200-781 LISBON, PORTUGAL
Web page: https://aquila1.iseg.ulisboa.pt/aquila/departamentos/EC

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Keywords: Matching; College Admissions Problem; Stability; Random Mechanism.;

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  1. 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.
  2. Herve Moulin, 2004. "Fair Division and Collective Welfare," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262633116, December.
  3. Pais, Joana, 2008. "Incentives in decentralized random matching markets," Games and Economic Behavior, Elsevier, vol. 64(2), pages 632-649, November.
  4. 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.
  5. Joana Pais, 2006. "On Random Matching Markets: Properties and Equilibria," Working Papers Department of Economics 2006/11, ISEG - School of Economics and Management, Department of Economics, University of Lisbon.
  6. Abdulkadiroglu, Atila & Sonmez, Tayfun, 1999. "House Allocation with Existing Tenants," Journal of Economic Theory, Elsevier, vol. 88(2), pages 233-260, October.
  7. 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).
  8. 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.
  9. Dipjyoti Majumdar, 2003. "Ordinally Bayesian Incentive Compatible Stable Matching," Working Papers hal-00242988, HAL.
  10. 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.
  11. Moulin, HervÈ, 1997. "Procedural cum Endstate Justice: An Implementation Viewpoint," Working Papers 97-17, Duke University, Department of Economics.
  12. Dipjyoti Majumdar & Arunava Sen, 2004. "Ordinally Bayesian Incentive Compatible Voting Rules," Econometrica, Econometric Society, vol. 72(2), pages 523-540, 03.
  13. 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.
  14. 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.
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Cited by:
  1. Joana Pais, 2006. "Incentives in Decentralized Random Matching Markets," Working Papers Department of Economics 2006/12, ISEG - School of Economics and Management, Department of Economics, University of Lisbon.
  2. Guillaume Haeringer & Flip Klijn, 2008. "Constrained School Choice," Working Papers 294, Barcelona Graduate School of Economics.
  3. Been-Lon Chen & Jie-Ping Mo & Ping Wang, 2012. "Two-sided micro-matching with technical progress," Economic Theory, Springer, vol. 50(2), pages 445-462, June.
  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.
  5. Alexander Westkamp, 2013. "An analysis of the German university admissions system," Economic Theory, Springer, vol. 53(3), pages 561-589, August.
  6. 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.

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