IDEAS home Printed from https://ideas.repec.org/a/the/publsh/5088.html
   My bibliography  Save this article

Optimal assignment mechanisms with imperfect verification

Author

Listed:
  • Pereyra, Juan Sebastián

    (Department of Economics, Universidad de la Republica)

  • Silva, Francisco

    (Department of Economics, Deakin University)

Abstract

Objects of different quality are to be allocated to agents. Agents can receive at most one object, and there are not enough high-quality objects for every agent. The value to the social planner from allocating objects to any given agent depends on that agent's private information. The social planner is unable to use transfers to give incentives for agents to convey their private information. Instead, she is able to imperfectly verify their reports through signals that are positively affiliated with each agent's type. We characterize mechanisms that maximize the social planner's expected payoff. In the optimal mechanism, each agent chooses one of various tracks, which are characterized by two thresholds. If the agent's signal exceeds the upper threshold of the chosen track, the agent receives a high-quality object, if it is in-between the two thresholds, he receives a low-quality object and if it is below the lower threshold, he receives no object.

Suggested Citation

  • Pereyra, Juan Sebastián & Silva, Francisco, 2023. "Optimal assignment mechanisms with imperfect verification," Theoretical Economics, Econometric Society, vol. 18(2), May.
    • Handle: RePEc:the:publsh:5088
    as

    Download full text from publisher

    File URL: http://econtheory.org/ojs/index.php/te/article/viewFile/20230793/36537/1102
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Judd, Kenneth L., 1985. "The law of large numbers with a continuum of IID random variables," Journal of Economic Theory, Elsevier, vol. 35(1), pages 19-25, February.
    2. Deniz Kattwinkel, 2020. "Allocation With Correlated Information: Too Good to Be True," CRC TR 224 Discussion Paper Series crctr224_2020_227, University of Bonn and University of Mannheim, Germany.
    3. Pietro Ortoleva & Evgenii Safonov & Leeat Yariv, 2021. "Who Cares More? Allocation with Diverse Preference Intensities," Working Papers 2021-10, Princeton University. Economics Department..
    4. Bogomolnaia, Anna & Moulin, Herve, 2001. "A New Solution to the Random Assignment Problem," Journal of Economic Theory, Elsevier, vol. 100(2), pages 295-328, October.
    5. Anke S. Kessler & Christoph Lülfesmann & Patrick W. Schmitz, 2005. "Endogenous Punishments In Agency With Verifiable Ex Post Information ," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 46(4), pages 1207-1231, November.
    6. Silva, Francisco, 2019. "Renegotiation proof mechanism design with imperfect type verification," Theoretical Economics, Econometric Society, vol. 14(3), July.
    7. 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.
    8. Bose, Subir & Zhao, Jinhua, 2007. "Optimal use of correlated information in mechanism design when full surplus extraction may be impossible," Journal of Economic Theory, Elsevier, vol. 135(1), pages 357-381, July.
    9. Tymofiy Mylovanov & Andriy Zapechelnyuk, 2017. "Optimal Allocation with Ex Post Verification and Limited Penalties," American Economic Review, American Economic Association, vol. 107(9), pages 2666-2694, September.
    10. Erlanson, Albin & Kleiner, Andreas, 2020. "Costly verification in collective decisions," Theoretical Economics, Econometric Society, vol. 15(3), July.
    11. Calsamiglia, Caterina & Güell, Maia, 2018. "Priorities in school choice: The case of the Boston mechanism in Barcelona," Journal of Public Economics, Elsevier, vol. 163(C), pages 20-36.
    12. Lien, Jaimie W. & Zheng, Jie & Zhong, Xiaohan, 2017. "Ex-ante fairness in the Boston and serial dictatorship mechanisms under pre-exam and post-exam preference submission," Games and Economic Behavior, Elsevier, vol. 101(C), pages 98-120.
    13. Riordan, Michael H. & Sappington, David E. M., 1988. "Optimal contracts with public ex post information," Journal of Economic Theory, Elsevier, vol. 45(1), pages 189-199, June.
    14. Francisco Silva, 2020. "The Importance of Commitment Power in Games with Imperfect Evidence," American Economic Journal: Microeconomics, American Economic Association, vol. 12(4), pages 99-113, November.
    15. Balinski, Michel & Sonmez, Tayfun, 1999. "A Tale of Two Mechanisms: Student Placement," Journal of Economic Theory, Elsevier, vol. 84(1), pages 73-94, January.
    16. Cremer, Jacques & McLean, Richard P, 1988. "Full Extraction of the Surplus in Bayesian and Dominant Strategy Auctions," Econometrica, Econometric Society, vol. 56(6), pages 1247-1257, November.
    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. Bloch, Francis & Dutta, Bhaskar & Dziubiński, Marcin, 2023. "Selecting a winner with external referees," Journal of Economic Theory, Elsevier, vol. 211(C).

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Francisco Silva & Juan Pereyra, 2020. "Optimal object assignment mechanisms with imperfect type veri?cation," Documentos de Trabajo 540, Instituto de Economia. Pontificia Universidad Católica de Chile..
    2. Chillemi, Ottorino & Galavotti, Stefano & Gui, Benedetto, 2020. "Optimal contracts with contingent allocation," Economics Letters, Elsevier, vol. 192(C).
    3. Daniel Danau & Annalisa Vinella, 2020. "A note on optimal contracting with public ex post information under limited liability," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(1), pages 47-74, March.
    4. Daniel Danau & Analisa Vinella, 2016. "On the optimal use of correlated information in contractual design under limited liability," Economics Working Paper Archive (University of Rennes 1 & University of Caen) 2016-05, Center for Research in Economics and Management (CREM), University of Rennes 1, University of Caen and CNRS.
    5. Robert Gary‐Bobo & Yossi Spiegel, 2006. "Optimal state‐contingent regulation under limited liability," RAND Journal of Economics, RAND Corporation, vol. 37(2), pages 431-448, June.
    6. Roland Strausz, 2006. "Interim Information in Long‐Term Contracts," Journal of Economics & Management Strategy, Wiley Blackwell, vol. 15(4), pages 1041-1067, December.
    7. Kojima, Fuhito, 2013. "Efficient resource allocation under multi-unit demand," Games and Economic Behavior, Elsevier, vol. 82(C), pages 1-14.
    8. Kesten, Onur & Unver, Utku, 2015. "A theory of school choice lotteries," Theoretical Economics, Econometric Society, vol. 10(2), May.
    9. Mikhail Drugov, 2010. "Information and delay in an agency model," RAND Journal of Economics, RAND Corporation, vol. 41(3), pages 598-615, September.
    10. Nikhil Agarwal & Eric Budish, 2021. "Market Design," NBER Working Papers 29367, National Bureau of Economic Research, Inc.
    11. Daniel Danau & Annalisa Vinella, 2017. "Contractual design in agency problems with non-monotonic cost and correlated information," SERIES 02-2017, Dipartimento di Economia e Finanza - Università degli Studi di Bari "Aldo Moro", revised Mar 2017.
    12. Yeon-Koo Che & Fuhito Kojima, 2010. "Asymptotic Equivalence of Probabilistic Serial and Random Priority Mechanisms," Econometrica, Econometric Society, vol. 78(5), pages 1625-1672, September.
    13. Fuhito Kojima & M. Ünver, 2014. "The “Boston” school-choice mechanism: an axiomatic approach," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 55(3), pages 515-544, April.
    14. Ottorino Chillemi & Stefano Galavotti & Benefetto Gui, 2017. "Inefficient Rationing With Post-Contractual Information," "Marco Fanno" Working Papers 0214, Dipartimento di Scienze Economiche "Marco Fanno".
    15. José Alcalde & Antonio Romero-Medina, 2017. "Fair student placement," Theory and Decision, Springer, vol. 83(2), pages 293-307, August.
    16. Dur, Umut & Hammond, Robert G. & Kesten, Onur, 2021. "Sequential school choice: Theory and evidence from the field and lab," Journal of Economic Theory, Elsevier, vol. 198(C).
    17. Afacan, Mustafa Oǧuz, 2018. "The object allocation problem with random priorities," Games and Economic Behavior, Elsevier, vol. 110(C), pages 71-89.
    18. Hernandez-Chanto Allan, 2020. "College Assignment Problems Under Constrained Choice, Private Preferences, and Risk Aversion," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 20(2), pages 1-20, June.
    19. Basteck, Christian & Klaus, Bettina & Kübler, Dorothea, 2021. "How lotteries in school choice help to level the playing field," Games and Economic Behavior, Elsevier, vol. 129(C), pages 198-237.
    20. Yannai A. Gonczarowski & Michael Yin & Shirley Zhang, 2024. "Multi-District School Choice: Playing on Several Fields," Papers 2403.04530, arXiv.org.

    More about this item

    Keywords

    Imperfect verification; evidence; mechanism design; matching;
    All these keywords.

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • D8 - Microeconomics - - Information, Knowledge, and Uncertainty

    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:the:publsh:5088. See general information about how to correct material in RePEc.

    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 bibliographic 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.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Martin J. Osborne (email available below). General contact details of provider: http://econtheory.org .

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

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.