IDEAS home Printed from https://ideas.repec.org/p/swe/wpaper/2018-11.html
   My bibliography  Save this paper

Implementing the Median

Author

Listed:
  • Matías Núñez

    () (Universitè Paris-Dauphine, PSL Research University, CNRS, Lamsade)

  • Carlos Pimienta

    () (School of Economics, UNSW Business School)

  • Dimitrios Xefteris

    () (University of Cyprus, Department of Economics)

Abstract

In the single-peaked domain, the median rules (Moulin, 1980) are of special interest. They are, essentially, the unique strategy-proof rules as well as the unique Nash implementable ones under complete information. We show that, under mild assumptions on admissible priors, they are also Bayes-Nash implementable by the means of ``detail-free'' mechanisms. That is, mechanisms that do not rely on the mechanism designer having detailed information about the priors that the agents hold. Furthermore, detail-free implementation of the median rules does not clash with truthful behavior. The provided mechanism is such that, in every equilibrium, all agents reveal their true peak with probability one.

Suggested Citation

  • Matías Núñez & Carlos Pimienta & Dimitrios Xefteris, 2018. "Implementing the Median," Discussion Papers 2018-11, School of Economics, The University of New South Wales.
  • Handle: RePEc:swe:wpaper:2018-11
    as

    Download full text from publisher

    File URL: http://research.economics.unsw.edu.au/RePEc/papers/2018-11.pdf
    Download Restriction: no

    References listed on IDEAS

    as
    1. Chatterji, Shurojit & Sen, Arunava & Zeng, Huaxia, 2016. "A characterization of single-peaked preferences via random social choice functions," Theoretical Economics, Econometric Society, vol. 11(2), May.
    2. Dolors Berga & Bernardo Moreno, 2009. "Strategic requirements with indifference: single-peaked versus single-plateaued preferences," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 32(2), pages 275-298, February.
    3. Dirk Bergemann & Stephen Morris, 2005. "Robust Mechanism Design," Econometrica, Econometric Society, vol. 73(6), pages 1771-1813, November.
    4. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
    5. Benoît, Jean-Pierre & Ok, Efe A., 2008. "Nash implementation without no-veto power," Games and Economic Behavior, Elsevier, vol. 64(1), pages 51-67, September.
    6. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-477, March.
    7. Cason, Timothy N. & Saijo, Tatsuyoshi & Sjostrom, Tomas & Yamato, Takehiko, 2006. "Secure implementation experiments: Do strategy-proof mechanisms really work?," Games and Economic Behavior, Elsevier, vol. 57(2), pages 206-235, November.
    8. Chatterji, Shurojit & Sen, Arunava & Zeng, Huaxia, 2016. "A characterization of single-peaked preferences via random social choice functions," Economics and Statistics Working Papers 11-2016, Singapore Management University, School of Economics.
    9. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2017. "Optimal Voting Rules," Review of Economic Studies, Oxford University Press, vol. 84(2), pages 688-717.
    10. Arribillaga, R. Pablo & Massó, Jordi, 2016. "Comparing generalized median voter schemes according to their manipulability," Theoretical Economics, Econometric Society, vol. 11(2), May.
    11. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 65(5), pages 1175-1200, September.
    12. repec:eee:jetheo:v:170:y:2017:i:c:p:169-181 is not listed on IDEAS
    13. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
    14. Yves Sprumont, 1995. "Strategyproof Collective Choice in Economic and Political Environments," Canadian Journal of Economics, Canadian Economics Association, vol. 28(1), pages 68-107, February.
    15. Hirofumi Yamamura & Ryo Kawasaki, 2013. "Generalized average rules as stable Nash mechanisms to implement generalized median rules," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 40(3), pages 815-832, March.
    Full references (including those not matched with items on IDEAS)

    More about this item

    Keywords

    Nash Implementation; Bayesian Implementation; Robust Implementation; Detail-free; Median rule; Strategy-proofness; Single-Peaked Preferences; Condorcet Winner.;

    JEL classification:

    • C9 - Mathematical and Quantitative Methods - - Design of Experiments
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • H41 - Public Economics - - Publicly Provided Goods - - - Public Goods

    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:swe:wpaper:2018-11. 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: (Hongyi Li). General contact details of provider: http://edirc.repec.org/data/senswau.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.