IDEAS home Printed from https://ideas.repec.org/a/spr/reecde/v26y2022i4d10.1007_s10058-022-00289-4.html
   My bibliography  Save this article

Ordinal Bayesian incentive compatibility in random assignment model

Author

Listed:
  • Sulagna Dasgupta

    (University of Chicago)

  • Debasis Mishra

    (Indian Statistical Institute, Delhi)

Abstract

We explore the consequences of weakening the notion of incentive compatibility from strategy-proofness to ordinal Bayesian incentive compatibility (OBIC) in the random assignment model. If the common prior of the agents is the uniform prior, then a large class of random mechanisms are OBIC with respect to this prior—this includes the probabilistic serial mechanism. We then introduce a robust version of OBIC: a mechanism is locally robust OBIC if it is OBIC with respect all independent and identical priors in some neighborhood of a given independent and identical prior. We show that every locally robust OBIC mechanism satisfying a mild property called elementary monotonicity is strategy-proof. This leads to a strengthening of the impossibility result in Bogomolnaia and Moulin (J Econ Theory 100:295–328, 2001): if there are at least four agents, there is no locally robust OBIC and ordinally efficient mechanism satisfying equal treatment of equals.

Suggested Citation

  • Sulagna Dasgupta & Debasis Mishra, 2022. "Ordinal Bayesian incentive compatibility in random assignment model," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 651-664, December.
    • Handle: RePEc:spr:reecde:v:26:y:2022:i:4:d:10.1007_s10058-022-00289-4
    DOI: 10.1007/s10058-022-00289-4
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s10058-022-00289-4
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s10058-022-00289-4?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    References listed on IDEAS

    as
    1. d’ASPREMONT, C. & PELEG, B., 1986. "Ordinal Bayesian incentive compatible representations of committees," LIDAM Discussion Papers CORE 1986042, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    2. Miralles, Antonio, 2012. "Cardinal Bayesian allocation mechanisms without transfers," Journal of Economic Theory, Elsevier, vol. 147(1), pages 179-206.
    3. Ledyard, John O., 1978. "Incentive compatibility and incomplete information," Journal of Economic Theory, Elsevier, vol. 18(1), pages 171-189, June.
    4. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 2, pages 49-96, World Scientific Publishing Co. Pte. Ltd..
    5. 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.
    6. Mishra, Debasis, 2016. "Ordinal Bayesian incentive compatibility in restricted domains," Journal of Economic Theory, Elsevier, vol. 163(C), pages 925-954.
    7. Kojima, Fuhito & Manea, Mihai, 2010. "Incentives in the probabilistic serial mechanism," Journal of Economic Theory, Elsevier, vol. 145(1), pages 106-123, January.
    8. 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.
    9. Liu, Peng, 2020. "Random assignments on sequentially dichotomous domains," Games and Economic Behavior, Elsevier, vol. 121(C), pages 565-584.
    10. Ivan Balbuzanov, 2016. "Convex strategyproofness with an application to the probabilistic serial mechanism," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 46(3), pages 511-520, March.
    11. Mennle, Timo & Seuken, Sven, 2021. "Partial strategyproofness: Relaxing strategyproofness for the random assignment problem," Journal of Economic Theory, Elsevier, vol. 191(C).
    12. Katta, Akshay-Kumar & Sethuraman, Jay, 2006. "A solution to the random assignment problem on the full preference domain," Journal of Economic Theory, Elsevier, vol. 131(1), pages 231-250, November.
    13. Wonki Jo Cho, 2018. "Probabilistic assignment: an extension approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(1), pages 137-162, June.
    14. Bogomolnaia, Anna & Heo, Eun Jeong, 2012. "Probabilistic assignment of objects: Characterizing the serial rule," Journal of Economic Theory, Elsevier, vol. 147(5), pages 2072-2082.
    15. Miho Hong & Semin Kim, 2018. "Unanimity and Local Incentive Compatibility," Working papers 2018rwp-138, Yonsei University, Yonsei Economics Research Institute.
    16. 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.
    17. Gibbard, Allan, 1977. "Manipulation of Schemes That Mix Voting with Chance," Econometrica, Econometric Society, vol. 45(3), pages 665-681, April.
    18. Hashimoto, Tadashi & Hirata, Daisuke & Kesten, Onur & Kurino, Morimitsu & Unver, Utku, 2014. "Two axiomatic approaches to the probabilistic serial mechanism," Theoretical Economics, Econometric Society, vol. 9(1), January.
    19. Satterthwaite, Mark Allen, 1975. "Strategy-proofness and Arrow's conditions: Existence and correspondence theorems for voting procedures and social welfare functions," Journal of Economic Theory, Elsevier, vol. 10(2), pages 187-217, April.
    20. Liu, Peng & Zeng, Huaxia, 2019. "Random assignments on preference domains with a tier structure," Journal of Mathematical Economics, Elsevier, vol. 84(C), pages 176-194.
    21. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    Full references (including those not matched with items on IDEAS)

    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. Sulagna Dasgupta & Debasis Mishra, 2020. "Ordinal Bayesian incentive compatibility in random assignment model," Papers 2009.13104, arXiv.org, revised May 2021.
    2. Cho, Wonki Jo, 2016. "Incentive properties for ordinal mechanisms," Games and Economic Behavior, Elsevier, vol. 95(C), pages 168-177.
    3. Basteck, Christian & Ehlers, Lars, 2023. "Strategy-proof and envy-free random assignment," Journal of Economic Theory, Elsevier, vol. 209(C).
    4. Balbuzanov, Ivan, 2022. "Constrained random matching," Journal of Economic Theory, Elsevier, vol. 203(C).
    5. Wonki Jo Cho, 2018. "Probabilistic assignment: an extension approach," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 51(1), pages 137-162, June.
    6. Hougaard, Jens Leth & Moreno-Ternero, Juan D. & Østerdal, Lars Peter, 2014. "Assigning agents to a line," Games and Economic Behavior, Elsevier, vol. 87(C), pages 539-553.
    7. Shende, Priyanka & Purohit, Manish, 2023. "Strategy-proof and envy-free mechanisms for house allocation," Journal of Economic Theory, Elsevier, vol. 213(C).
    8. Basteck, Christian & Ehlers, Lars H., 2022. "Strategy-proof and envy-free random assignment," Discussion Papers, Research Unit: Market Behavior SP II 2022-208, WZB Berlin Social Science Center.
    9. Basteck, Christian & Ehlers, Lars, 2021. "Strategy-Proof and Envy-Free Random Assignment," Rationality and Competition Discussion Paper Series 307, CRC TRR 190 Rationality and Competition.
    10. Aziz, Haris & Brandl, Florian & Brandt, Felix & Brill, Markus, 2018. "On the tradeoff between efficiency and strategyproofness," Games and Economic Behavior, Elsevier, vol. 110(C), pages 1-18.
    11. Ehlers, Lars & Majumdar, Dipjyoti & Mishra, Debasis & Sen, Arunava, 2020. "Continuity and incentive compatibility in cardinal mechanisms," Journal of Mathematical Economics, Elsevier, vol. 88(C), pages 31-41.
    12. Cho, Wonki Jo, 2016. "When is the probabilistic serial assignment uniquely efficient and envy-free?," Journal of Mathematical Economics, Elsevier, vol. 66(C), pages 14-25.
    13. Haris Aziz & Yoichi Kasajima, 2017. "Impossibilities for probabilistic assignment," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 49(2), pages 255-275, August.
    14. Bogomolnaia, Anna & Moulin, Herve, 2015. "Size versus fairness in the assignment problem," Games and Economic Behavior, Elsevier, vol. 90(C), pages 119-127.
    15. Marek Pycia & Peter Troyan, 2023. "A Theory of Simplicity in Games and Mechanism Design," Econometrica, Econometric Society, vol. 91(4), pages 1495-1526, July.
    16. Chang, Hee-In & Chun, Youngsub, 2017. "Probabilistic assignment of indivisible objects when agents have the same preferences except the ordinal ranking of one object," Mathematical Social Sciences, Elsevier, vol. 90(C), pages 80-92.
    17. Andrew McLennan & Shino Takayama & Yuki Tamura, 2024. "An Efficient, Computationally Tractable School Choice Mechanism," Discussion Papers Series 668, School of Economics, University of Queensland, Australia.
    18. Anna Bogomolnaia, 2015. "The Most Ordinally-Efficient of Random Voting Rules," HSE Working papers WP BRP 106/EC/2015, National Research University Higher School of Economics.
    19. Mennle, Timo & Seuken, Sven, 2021. "Partial strategyproofness: Relaxing strategyproofness for the random assignment problem," Journal of Economic Theory, Elsevier, vol. 191(C).
    20. Brandl, Florian & Brandt, Felix & Suksompong, Warut, 2016. "The impossibility of extending random dictatorship to weak preferences," Economics Letters, Elsevier, vol. 141(C), pages 44-47.

    More about this item

    Keywords

    Ordinal Bayesian incentive compatibility; Random assignment; Probabilistic serial mechanism;
    All these keywords.

    JEL classification:

    • D47 - Microeconomics - - Market Structure, Pricing, and Design - - - Market Design
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

    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:spr:reecde:v:26:y:2022:i:4:d:10.1007_s10058-022-00289-4. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.