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Incomplete Information and Small Cores in Matching Markets

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  • Lars Ehlers
  • Jordi Massó

Abstract

We study Bayesian Nash equilibria of stable mechanisms in centralized matching markets under incomplete information. We show that truth-telling is a Bayesian Nash equilibrium of the revelation game induced by a common belief and a stable mechanism if and only if all the profiles in the support of the common belief have singleton cores. Our result matches the observations of Roth and Peranson (1999) in the National Resident Matching Program (NRMP) in the United States: (i) the cores of the profiles submitted to the clearinghouse are small and (ii) while truth-telling is not a dominant strategy most participants of the NRMP truthfully reveal their preferences.

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Bibliographic Info

Paper provided by Barcelona Graduate School of Economics in its series Working Papers with number 147.

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Date of creation: Oct 2004
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Handle: RePEc:bge:wpaper:147

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Keywords: Matching Market; Incomplete Information; Small Core;

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  1. EHLERS, Lars, 2003. "In Search of Advice for Physicians in Entry-Level Medical Markets," Cahiers de recherche 13-2003, Centre interuniversitaire de recherche en économie quantitative, CIREQ.
  2. Ehlers, Lars, 2004. "In search of advice for participants in matching markets which use the deferred-acceptance algorithm," Games and Economic Behavior, Elsevier, vol. 48(2), pages 249-270, August.
  3. Dutta, Bhaskar & Masso, Jordi, 1997. "Stability of Matchings When Individuals Have Preferences over Colleagues," Journal of Economic Theory, Elsevier, vol. 75(2), pages 464-475, August.
  4. Bettina Klaus & Flip Klijn & Jordi Massó, 2007. "Some things couples always wanted to know about stable matchings (but were afraid to ask)," Review of Economic Design, Springer, vol. 11(3), pages 175-184, November.
  5. Dipjyoti Majumdar & Arunava Sen, 2004. "Ordinally Bayesian Incentive Compatible Voting Rules," Econometrica, Econometric Society, vol. 72(2), pages 523-540, 03.
  6. Roth,Alvin E. & Sotomayor,Marilda A. Oliveira, 1992. "Two-Sided Matching," Cambridge Books, Cambridge University Press, number 9780521437882, November.
  7. Alvin E. Roth & Elliott Peranson, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," NBER Working Papers 6963, National Bureau of Economic Research, Inc.
  8. Simon Clark, 2004. "Uniqueness of Equilibrium in Two-sided Matching," ESE Discussion Papers 84, Edinburgh School of Economics, University of Edinburgh.
  9. repec:ebl:ecbull:v:3:y:2004:i:45:p:1-11 is not listed on IDEAS
  10. 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).
  11. 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.
  12. Roth, Alvin E., 1984. "Misrepresentation and stability in the marriage problem," Journal of Economic Theory, Elsevier, vol. 34(2), pages 383-387, December.
  13. Roth, Alvin E & Xing, Xiaolin, 1994. "Jumping the Gun: Imperfections and Institutions Related to the Timing of Market Transactions," American Economic Review, American Economic Association, vol. 84(4), pages 992-1044, September.
  14. Muriel Niederle & Alvin E. Roth, 2003. "Unraveling Reduces Mobility in a Labor Market: Gastroenterology with and without a Centralized Match," Journal of Political Economy, University of Chicago Press, vol. 111(6), pages 1342-1352, December.
  15. Alvin E. Roth, 2002. "The Economist as Engineer: Game Theory, Experimentation, and Computation as Tools for Design Economics," Econometrica, Econometric Society, vol. 70(4), pages 1341-1378, July.
  16. Eeckhout, Jan, 2000. "On the uniqueness of stable marriage matchings," Economics Letters, Elsevier, vol. 69(1), pages 1-8, October.
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