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Matching Markets under (In)complete Information

  • EHLERS, Lars
  • MASSÓ, Jordi

We are the first to introduce incomplete information to centralized many-to-one matching markets such as those to entry-level labor markets or college admissions. This is important because in real life markets (i) any agent is uncertain about the other agents' true preferences and (ii) most entry-level matching is many-to-one (and not one-to-one). We show that for stable (matching) mechanisms there is a strong and surprising link between Nash equilibria under complete information and Bayesian Nash equilibria under incomplete information. That is,given a common belief, a strategy profile is a Bayesian Nash equilibrium under incomplete information in a stable mechanism if and only if, for any true profile in the support of the common belief, the submitted profile is a Nash equilibrium under complete information at the true profile in the direct preference revelation game induced by the stable mechanism. This result may help to explain the success of stable mechanisms in these markets.

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File URL: http://hdl.handle.net/1866/721
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Paper provided by Universite de Montreal, Departement de sciences economiques in its series Cahiers de recherche with number 2007-01.

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Date of creation: 2007
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Handle: RePEc:mtl:montde:2007-01
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  1. 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.
  2. Dipjyoti Majumdar, 2003. "Ordinally Bayesian Incentive Compatible Stable Matching," Working Papers hal-00242988, HAL.
  3. 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.
  4. Pathak, Parag A. & Abdulkadiroglu, Atila & Roth, Alvin, 2005. "The New York City High School Match," Scholarly Articles 2562765, Harvard University Department of Economics.
  5. 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.
  6. Yan Chen & Tayfun Sönmez, 2004. "School Choice: An Experimental Study," Boston College Working Papers in Economics 622, Boston College Department of Economics.
  7. EHLERS, Lars, 2003. "In Search of Advice for Physicians in Entry-Level Medical Markets," Cahiers de recherche 2003-15, Universite de Montreal, Departement de sciences economiques.
  8. Crawford, Vincent P., 1991. "Comparative statics in matching markets," Journal of Economic Theory, Elsevier, vol. 54(2), pages 389-400, August.
  9. 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.
  10. José Alcalde, 1995. "Implementation of Stable Solutions to Marriage Problems," Working Papers. Serie AD 1995-05, Instituto Valenciano de Investigaciones Económicas, S.A. (Ivie).
  11. Sonmez, Tayfun, 1997. "Games of Manipulation in Marriage Problems," Games and Economic Behavior, Elsevier, vol. 20(2), pages 169-176, August.
  12. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
  13. Dipjyoti Majumdar & Arunava Sen, 2004. "Ordinally Bayesian Incentive Compatible Voting Rules," Econometrica, Econometric Society, vol. 72(2), pages 523-540, 03.
  14. Shin, Sungwhee & Suh, Sang-Chul, 1996. "A mechanism implementing the stable rule in marriage problems," Economics Letters, Elsevier, vol. 51(2), pages 185-189, May.
  15. Antonio Romero-Medina, 1998. "Implementation of stable solutions in a restricted matching market," Review of Economic Design, Springer, vol. 3(2), pages 137-147.
  16. Roth, Alvin E., 1984. "Misrepresentation and stability in the marriage problem," Journal of Economic Theory, Elsevier, vol. 34(2), pages 383-387, December.
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