IDEAS home Printed from https://ideas.repec.org/p/mtl/montde/2007-01.html
   My bibliography  Save this paper

Matching Markets under (In)complete Information

Author

Listed:
  • EHLERS, Lars
  • MASSÓ, Jordi

Abstract

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.

Suggested Citation

  • EHLERS, Lars & MASSÓ, Jordi, 2007. "Matching Markets under (In)complete Information," Cahiers de recherche 2007-01, Universite de Montreal, Departement de sciences economiques.
  • Handle: RePEc:mtl:montde:2007-01
    as

    Download full text from publisher

    File URL: http://hdl.handle.net/1866/721
    Download Restriction: no

    Other versions of this item:

    References listed on IDEAS

    as
    1. Dipjyoti Majumdar, 2003. "Ordinally Bayesian Incentive Compatible Stable Matching," Working Papers hal-00242988, HAL.
    2. Joana Pais, 2008. "Random matching in the college admissions problem," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 35(1), pages 99-116, April.
    3. Atila Abdulkadiroğlu & Parag A. Pathak & Alvin E. Roth, 2005. "The New York City High School Match," American Economic Review, American Economic Association, vol. 95(2), pages 364-367, May.
    4. 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.
    5. Alcalde, Jose, 1996. "Implementation of Stable Solutions to Marriage Problems," Journal of Economic Theory, Elsevier, vol. 69(1), pages 240-254, April.
    6. Ergin, Haluk & Sonmez, Tayfun, 2006. "Games of school choice under the Boston mechanism," Journal of Public Economics, Elsevier, vol. 90(1-2), pages 215-237, January.
    7. Roth, Alvin E., 1989. "Two-sided matching with incomplete information about others' preferences," Games and Economic Behavior, Elsevier, vol. 1(2), pages 191-209, June.
    8. 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.
    9. Chakraborty, Archishman & Citanna, Alessandro & Ostrovsky, Michael, 2010. "Two-sided matching with interdependent values," Journal of Economic Theory, Elsevier, vol. 145(1), pages 85-105, January.
    10. Chen, Yan & Sonmez, Tayfun, 2006. "School choice: an experimental study," Journal of Economic Theory, Elsevier, vol. 127(1), pages 202-231, March.
    11. 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.
    12. Muriel Niederle & Alvin E. Roth, 2001. "Unraveling Reduces the Scope of an Entry Level Labor Market: Gastroenterology With and Without a Centralized Match," NBER Working Papers 8616, National Bureau of Economic Research, Inc.
    13. Atila Abdulkadiroglu & Yeon-Koo Che & Yosuke Yasuda, 2011. "Resolving Conflicting Preferences in School Choice: The "Boston Mechanism" Reconsidered," American Economic Review, American Economic Association, vol. 101(1), pages 399-410, February.
    14. 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.
    15. Roth, Alvin 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, American Economic Association, vol. 81(3), pages 415-440, June.
    16. Shouyong Shi, 2002. "A Directed Search Model of Inequality with Heterogeneous Skills and Skill-Biased Technology," Review of Economic Studies, Oxford University Press, vol. 69(2), pages 467-491.
    17. Antonio Romero-Medina, 1998. "Implementation of stable solutions in a restricted matching market," Review of Economic Design, Springer;Society for Economic Design, vol. 3(2), pages 137-147.
    18. Sonmez, Tayfun, 1997. "Games of Manipulation in Marriage Problems," Games and Economic Behavior, Elsevier, vol. 20(2), pages 169-176, August.
    19. Atila Abdulkadiroglu & Tayfun Sönmez, 2003. "School Choice: A Mechanism Design Approach," American Economic Review, American Economic Association, vol. 93(3), pages 729-747, June.
    20. Roth, Alvin E., 1984. "Misrepresentation and stability in the marriage problem," Journal of Economic Theory, Elsevier, vol. 34(2), pages 383-387, December.
    21. 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.
    22. Dipjyoti Majumdar & Arunava Sen, 2004. "Ordinally Bayesian Incentive Compatible Voting Rules," Econometrica, Econometric Society, vol. 72(2), pages 523-540, March.
    23. Ma Jinpeng, 1995. "Stable Matchings and Rematching-Proof Equilibria in a Two-Sided Matching Market," Journal of Economic Theory, Elsevier, vol. 66(2), pages 352-369, August.
    24. 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.
    25. Atila Abdulkadiroglu & Parag A. Pathak & Alvin E. Roth, 2009. "Strategy-Proofness versus Efficiency in Matching with Indifferences: Redesigning the NYC High School Match," American Economic Review, American Economic Association, vol. 99(5), pages 1954-1978, December.
    26. M. Utku Ünver, 2005. "On the survival of some unstable two-sided matching mechanisms," International Journal of Game Theory, Springer;Game Theory Society, vol. 33(2), pages 239-254, June.
    27. 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.
    28. Crawford, Vincent P., 1991. "Comparative statics in matching markets," Journal of Economic Theory, Elsevier, vol. 54(2), pages 389-400, August.
    29. Jinpeng Ma, 2002. "original papers : Stable matchings and the small core in Nash equilibrium in the college admissions problem," Review of Economic Design, Springer;Society for Economic Design, vol. 7(2), pages 117-134.
    30. Elliott Peranson & Alvin E. Roth, 1999. "The Redesign of the Matching Market for American Physicians: Some Engineering Aspects of Economic Design," American Economic Review, American Economic Association, vol. 89(4), pages 748-780, September.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Caterina Calsamiglia & Guillaume Haeringer & Flip Klijn, 2010. "Constrained School Choice: An Experimental Study," American Economic Review, American Economic Association, vol. 100(4), pages 1860-1874, September.
    2. repec:spr:jogath:v:46:y:2017:i:4:d:10.1007_s00182-016-0562-6 is not listed on IDEAS
    3. Eric Budish & Estelle Cantillon, 2012. "The Multi-unit Assignment Problem: Theory and Evidence from Course Allocation at Harvard," ULB Institutional Repository 2013/99376, ULB -- Universite Libre de Bruxelles.
    4. Mishra, Debasis, 2016. "Ordinal Bayesian incentive compatibility in restricted domains," Journal of Economic Theory, Elsevier, vol. 163(C), pages 925-954.
    5. Britta Hoyer & Nadja Stroh-Maraun, 2017. "Matching Strategies of Heterogeneous Agents under Incomplete Information in a University Clearinghouse," Working Papers CIE 110, Paderborn University, CIE Center for International Economics.

    More about this item

    Keywords

    Many-To-One Matching Market ; Incomete Information ; Stability;

    JEL classification:

    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D81 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Criteria for Decision-Making under Risk and Uncertainty
    • J44 - Labor and Demographic Economics - - Particular Labor Markets - - - Professional Labor Markets and Occupations

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:mtl:montde:2007-01. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sharon BREWER) or (Joanne Lustig). General contact details of provider: http://edirc.repec.org/data/demtlca.html .

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.