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Weak implementation

Author

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  • Kym Pram

    (University of Nevada, Reno)

Abstract

I define Weak Implementation under incomplete information. A social choice set is weakly implementable if the set of equilibrium outcomes of some mechanism is a non-empty subset of the social choice set. Weak implementation is a more natural objective than either full or partial implementation in many cases. I show that there are social choice sets where every subset can be weakly implemented, yet the set cannot be fully implemented. I give a complete characterization of the weakly implementable social choice sets under a weak restriction on preferences. As a corollary, I show that in independent private values environments the set of interim efficient social choice functions is weakly implementable whenever it is partially implementable.

Suggested Citation

  • Kym Pram, 2020. "Weak implementation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 69(3), pages 569-594, April.
    • Handle: RePEc:spr:joecth:v:69:y:2020:i:3:d:10.1007_s00199-019-01178-8
    DOI: 10.1007/s00199-019-01178-8
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    References listed on IDEAS

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    1. Thomas R. Palfrey & Sanjay Srivastava, 1987. "On Bayesian Implementable Allocations," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 54(2), pages 193-208.
    2. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Mechanism Design with Incomplete Information: A Solution to the Implementation Problem," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 668-691, June.
    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," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
    5. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-477, March.
    6. Tayfun Sönmez & Tarik Kara, 1997. "Implementation of college admission rules (*)," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 9(2), pages 197-218.
    7. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
    8. Serrano, Roberto & Vohra, Rajiv, 2010. "Multiplicity of mixed equilibria in mechanisms: A unified approach to exact and approximate implementation," Journal of Mathematical Economics, Elsevier, vol. 46(5), pages 775-785, September.
    9. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 65(5), pages 1175-1200, September.
    10. Brusco, Sandro, 1995. "Perfect Bayesian Implementation," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 5(3), pages 419-444, May.
    11. Bhaskar Dutta & Arunava Sen, 1994. "2-person Bayesian implementation," Review of Economic Design, Springer;Society for Economic Design, vol. 1(1), pages 41-54, December.
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    Cited by:

    1. Guo, Huiyi & Yannelis, Nicholas C., 2022. "Robust coalitional implementation," Games and Economic Behavior, Elsevier, vol. 132(C), pages 553-575.
    2. Zhiwei Liu & Nicholas C. Yannelis, 2021. "Persuasion in an asymmetric information economy: a justification of Wald’s maxmin preferences," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 72(3), pages 801-833, October.
    3. Liu, Zhiwei & Song, Xinxi & Yannelis, Nicholas C., 2020. "Randomization under ambiguity: Efficiency and incentive compatibility," Journal of Mathematical Economics, Elsevier, vol. 90(C), pages 1-11.
    4. Maria Gabriella Graziano & Claudia Meo & Nicholas C. Yannelis, 2020. "Shapley and Scarf housing markets with consumption externalities," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 22(5), pages 1481-1514, September.

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    More about this item

    Keywords

    Implementation theory; Mechanism design; Game theory; Full implementation;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations
    • D80 - Microeconomics - - Information, Knowledge, and Uncertainty - - - General
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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