IDEAS home Printed from https://ideas.repec.org/p/arx/papers/2009.13104.html
   My bibliography  Save this paper

Ordinal Bayesian incentive compatibility in random assignment model

Author

Listed:
  • Sulagna Dasgupta
  • Debasis Mishra

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 a 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 priors in some neighborhood of a given independent 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 (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, 2020. "Ordinal Bayesian incentive compatibility in random assignment model," Papers 2009.13104, arXiv.org, revised May 2021.
    • Handle: RePEc:arx:papers:2009.13104
    as

    Download full text from publisher

    File URL: http://arxiv.org/pdf/2009.13104
    File Function: Latest version
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Kojima, Fuhito & Manea, Mihai, 2010. "Incentives in the probabilistic serial mechanism," Journal of Economic Theory, Elsevier, vol. 145(1), pages 106-123, January.
    2. Szilvia Papai, 2000. "Strategyproof Assignment by Hierarchical Exchange," Econometrica, Econometric Society, vol. 68(6), pages 1403-1434, November.
    3. 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.
    4. 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).
    5. 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.
    6. Miho Hong & Semin Kim, 2018. "Unanimity and Local Incentive Compatibility," Working papers 2018rwp-138, Yonsei University, Yonsei Economics Research Institute.
    7. Pycia, Marek & Unver, Utku, 2017. "Incentive compatible allocation and exchange of discrete resources," Theoretical Economics, Econometric Society, vol. 12(1), January.
    8. 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.
    9. Dipjyoti Majumdar & Arunava Sen, 2004. "Ordinally Bayesian Incentive Compatible Voting Rules," Econometrica, Econometric Society, vol. 72(2), pages 523-540, March.
    10. Ledyard, John O., 1978. "Incentive compatibility and incomplete information," Journal of Economic Theory, Elsevier, vol. 18(1), pages 171-189, June.
    11. Cho, Wonki Jo, 2016. "Incentive properties for ordinal mechanisms," Games and Economic Behavior, Elsevier, vol. 95(C), pages 168-177.
    12. Lars-Gunnar Svensson, 1999. "Strategy-proof allocation of indivisible goods," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(4), pages 557-567.
    13. 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.
    14. 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.
    15. 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.
    16. 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.
    17. 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.
    18. Mishra, Debasis, 2016. "Ordinal Bayesian incentive compatibility in restricted domains," Journal of Economic Theory, Elsevier, vol. 163(C), pages 925-954.
    19. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    20. Gabriel Carroll, 2012. "When Are Local Incentive Constraints Sufficient?," Econometrica, Econometric Society, vol. 80(2), pages 661-686, March.
    21. 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.
    22. Bhargava, Mohit & , & ,, 2015. "Incentive-compatible voting rules with positively correlated beliefs," Theoretical Economics, Econometric Society, vol. 10(3), 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. Majumdar, Dipjyoti & Roy, Souvik, 2021. "Ordinally Bayesian incentive compatible probabilistic voting rules," Mathematical Social Sciences, Elsevier, vol. 114(C), pages 11-27.
    2. Mennle, Timo & Seuken, Sven, 2021. "Partial strategyproofness: Relaxing strategyproofness for the random assignment problem," Journal of Economic Theory, Elsevier, vol. 191(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. 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.
    2. Shende, Priyanka & Purohit, Manish, 2023. "Strategy-proof and envy-free mechanisms for house allocation," Journal of Economic Theory, Elsevier, vol. 213(C).
    3. 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.
    4. 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.
    5. Mishra, Debasis, 2016. "Ordinal Bayesian incentive compatibility in restricted domains," Journal of Economic Theory, Elsevier, vol. 163(C), pages 925-954.
    6. 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.
    7. Cho, Wonki Jo, 2016. "Incentive properties for ordinal mechanisms," Games and Economic Behavior, Elsevier, vol. 95(C), pages 168-177.
    8. Marek Pycia & M. Utku Ünver, 2022. "Outside options in neutral allocation of discrete resources," Review of Economic Design, Springer;Society for Economic Design, vol. 26(4), pages 581-604, December.
    9. Balbuzanov, Ivan, 2022. "Constrained random matching," Journal of Economic Theory, Elsevier, vol. 203(C).
    10. 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.
    11. Marek Pycia & Peter Troyan, 2023. "A Theory of Simplicity in Games and Mechanism Design," Econometrica, Econometric Society, vol. 91(4), pages 1495-1526, July.
    12. Monte, Daniel & Tumennasan, Norovsambuu, 2015. "Centralized allocation in multiple markets," Journal of Mathematical Economics, Elsevier, vol. 61(C), pages 74-85.
    13. 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.
    14. Altuntaş, Açelya & Phan, William & Tamura, Yuki, 2023. "Some characterizations of Generalized Top Trading Cycles," Games and Economic Behavior, Elsevier, vol. 141(C), pages 156-181.
    15. Mennle, Timo & Seuken, Sven, 2021. "Partial strategyproofness: Relaxing strategyproofness for the random assignment problem," Journal of Economic Theory, Elsevier, vol. 191(C).
    16. Liu, Peng, 2020. "Local vs. global strategy-proofness: A new equivalence result for ordinal mechanisms," Economics Letters, Elsevier, vol. 189(C).
    17. Youngsub Chun & Kiyong Yun, 2020. "Upper-contour strategy-proofness in the probabilistic assignment problem," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 54(4), pages 667-687, April.
    18. 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.
    19. 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.
    20. Basteck, Christian & Ehlers, Lars, 2023. "Strategy-proof and envy-free random assignment," Journal of Economic Theory, Elsevier, vol. 209(C).

    More about this item

    JEL classification:

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

    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:arx:papers:2009.13104. 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: arXiv administrators (email available below). General contact details of provider: http://arxiv.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.