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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
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    File URL: http://research.economics.unsw.edu.au/RePEc/papers/2018-11.pdf
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    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, 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..
    4. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, 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. Alex Gershkov & Benny Moldovanu & Xianwen Shi, 2017. "Optimal Voting Rules," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 84(2), pages 688-717.
    9. Arribillaga, R. Pablo & Massó, Jordi, 2016. "Comparing generalized median voter schemes according to their manipulability," Theoretical Economics, Econometric Society, vol. 11(2), May.
    10. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 65(5), pages 1175-1200, September.
    11. Núñez, Matías & Xefteris, Dimitrios, 2017. "Implementation via approval mechanisms," Journal of Economic Theory, Elsevier, vol. 170(C), pages 169-181.
    12. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
    13. 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.
    14. H. Moulin, 1980. "On strategy-proofness and single peakedness," Public Choice, Springer, vol. 35(4), pages 437-455, January.
    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.
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    More about this item

    Keywords

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

    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

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