IDEAS home Printed from https://ideas.repec.org/a/eee/jetheo/v163y2016icp925-954.html
   My bibliography  Save this article

Ordinal Bayesian incentive compatibility in restricted domains

Author

Listed:
  • Mishra, Debasis

Abstract

We study deterministic voting mechanisms by considering an ordinal notion of Bayesian incentive compatibility (OBIC). If the beliefs of agents are independent and generic, we show that a mechanism is OBIC and satisfies an additional condition called elementary monotonicity if and only if it is a dominant strategy incentive compatible mechanism. Our result works in a large class of preference domains (that include the unrestricted domain, the single-peaked domain, the single-dipped domain, and some single-crossing domains). We can significantly weaken elementary monotonicity in our result in the single-peaked domain if we assume unanimity and in a large class of domains if we assume unanimity and tops-onlyness.

Suggested Citation

  • Mishra, Debasis, 2016. "Ordinal Bayesian incentive compatibility in restricted domains," Journal of Economic Theory, Elsevier, vol. 163(C), pages 925-954.
  • Handle: RePEc:eee:jetheo:v:163:y:2016:i:c:p:925-954
    DOI: 10.1016/j.jet.2016.03.011
    as

    Download full text from publisher

    File URL: http://www.sciencedirect.com/science/article/pii/S0022053116300011
    Download Restriction: Full text for ScienceDirect subscribers only

    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. Dipjyoti Majumdar, 2003. "Ordinally Bayesian Incentive Compatible Stable Matching," Working Papers hal-00242988, HAL.
    2. Saporiti, Alejandro, 2009. "Strategy-proofness and single-crossing," Theoretical Economics, Econometric Society, vol. 4(2), June.
    3. Sato, Shin, 2013. "A sufficient condition for the equivalence of strategy-proofness and nonmanipulability by preferences adjacent to the sincere one," Journal of Economic Theory, Elsevier, vol. 148(1), pages 259-278.
    4. Salvador Barberà & Dolors Berga & Bernardo Moreno, 2012. "Domains, ranges and strategy-proofness: the case of single-dipped preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 39(2), pages 335-352, July.
    5. Demange, Gabrielle, 1982. "Single-peaked orders on a tree," Mathematical Social Sciences, Elsevier, vol. 3(4), pages 389-396, December.
    6. Börgers, Tilman & Smith, Doug, 2014. "Robust mechanism design and dominant strategy voting rules," Theoretical Economics, Econometric Society, vol. 9(2), May.
    7. Alexey Kushnir, 2013. "On the equivalence between Bayesian and dominant strategy implementation: the case of correlated types," ECON - Working Papers 129, Department of Economics - University of Zurich.
    8. John A. Weymark, 2008. "Strategy-Proofness and the Tops-Only Property," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 10(1), pages 7-26, February.
    9. Chatterji, Shurojit & Sanver, Remzi & Sen, Arunava, 2013. "On domains that admit well-behaved strategy-proof social choice functions," Journal of Economic Theory, Elsevier, vol. 148(3), pages 1050-1073.
    10. Mishra, Debasis & Pramanik, Anup & Roy, Souvik, 2016. "Local incentive compatibility with transfers," Games and Economic Behavior, Elsevier, vol. 100(C), pages 149-165.
    11. Dipjyoti Majumdar & Arunava Sen, 2004. "Ordinally Bayesian Incentive Compatible Voting Rules," Econometrica, Econometric Society, vol. 72(2), pages 523-540, March.
    12. Vikram Manjunath, 2014. "Efficient and strategy-proof social choice when preferences are single-dipped," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(3), pages 579-597, August.
    13. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    14. Börgers, Tilman & Postl, Peter, 2009. "Efficient compromising," Journal of Economic Theory, Elsevier, vol. 144(5), pages 2057-2076, September.
    15. Shurojit Chatterji & Arunava Sen, 2011. "Tops-only domains," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 46(2), pages 255-282, February.
    16. Alex Gershkov & Jacob K. Goeree & Alexey Kushnir & Benny Moldovanu & Xianwen Shi, 2013. "On the Equivalence of Bayesian and Dominant Strategy Implementation," Econometrica, Econometric Society, vol. 81(1), pages 197-220, January.
    17. 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.
    18. Ehlers, Lars & Massó, Jordi, 2015. "Matching markets under (in)complete information," Journal of Economic Theory, Elsevier, vol. 157(C), pages 295-314.
    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. Reffgen, Alexander, 2015. "Strategy-proof social choice on multiple and multi-dimensional single-peaked domains," Journal of Economic Theory, Elsevier, vol. 157(C), pages 349-383.
    21. Dipjyoti Majumdar & Arunava Sen, 2003. "Ordinally Bayesian incentive-compatible voting schemes," Indian Statistical Institute, Planning Unit, New Delhi Discussion Papers 03-01, Indian Statistical Institute, New Delhi, India.
    22. Alejandro M. Manelli & Daniel R. Vincent, 2010. "Bayesian and Dominant‐Strategy Implementation in the Independent Private‐Values Model," Econometrica, Econometric Society, vol. 78(6), pages 1905-1938, November.
    23. Gibbard, Allan, 1973. "Manipulation of Voting Schemes: A General Result," Econometrica, Econometric Society, vol. 41(4), pages 587-601, July.
    24. Gabriel Carroll, 2012. "When Are Local Incentive Constraints Sufficient?," Econometrica, Econometric Society, vol. 80(2), pages 661-686, March.
    25. Kalai, Ehud & Muller, Eitan, 1977. "Characterization of domains admitting nondictatorial social welfare functions and nonmanipulable voting procedures," Journal of Economic Theory, Elsevier, vol. 16(2), pages 457-469, December.
    26. Bhargava, Mohit & Majumdar, Dipjyoti & Sen, Arunava, 2015. "Incentive-compatible voting rules with positively correlated beliefs," Theoretical Economics, Econometric Society, vol. 10(3), September.
    27. Klaus, Bettina & Peters, Hans & Storcken, Ton, 1997. "Strategy-proof division of a private good when preferences are single-dipped," Economics Letters, Elsevier, vol. 55(3), pages 339-346, 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. Nozomu Muto & Shin Sato, 2016. "A decomposition of strategy-proofness," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 47(2), pages 277-294, August.
    2. repec:eee:gamebe:v:106:y:2017:i:c:p:1-15 is not listed on IDEAS

    More about this item

    Keywords

    Ordinal Bayesian incentive compatibility; Single-peaked domain; Elementary monotonicity;

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • 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:eee:jetheo:v:163:y:2016:i:c:p:925-954. 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: (Dana Niculescu). General contact details of provider: http://www.elsevier.com/locate/inca/622869 .

    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.