IDEAS home Printed from https://ideas.repec.org/a/spr/joecth/v69y2020i3d10.1007_s00199-019-01178-8.html
   My bibliography  Save this article

Weak implementation

Author

Listed:
  • 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
    as

    Download full text from publisher

    File URL: http://link.springer.com/10.1007/s00199-019-01178-8
    File Function: Abstract
    Download Restriction: Access to the full text of the articles in this series is restricted.
    File URL: https://libkey.io/10.1007/s00199-019-01178-8?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    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. 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," The Review of Economic Studies, Review of Economic Studies Ltd, 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.
    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. 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.
    5. Barlo, Mehmet & Dalkıran, Nuh Aygün, 2023. "Behavioral implementation under incomplete information," Journal of Economic Theory, Elsevier, vol. 213(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. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(4), pages 655-708.
    2. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare, in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288, Elsevier.
    3. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Working Papers 2003-19, Brown University, Department of Economics.
    4. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare,in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288 Elsevier.
    5. 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.
    6. Serrano, Roberto & Vohra, Rajiv, 2005. "A characterization of virtual Bayesian implementation," Games and Economic Behavior, Elsevier, vol. 50(2), pages 312-331, February.
    7. Roberto Serrano & Rajiv Vohra, 2000. "Type Diversity and Virtual Bayesian Implementation Creation-Date: 2000," Working Papers 2000-16, Brown University, Department of Economics.
    8. Bergemann, Dirk & Morris, Stephen & Takahashi, Satoru, 2017. "Interdependent preferences and strategic distinguishability," Journal of Economic Theory, Elsevier, vol. 168(C), pages 329-371.
    9. Dirk Bergemann & Stephen Morris, 2012. "Robust Implementation in General Mechanisms," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 5, pages 195-239, World Scientific Publishing Co. Pte. Ltd..
    10. Dirk Bergemann & Stephen Morris, 2005. "Robust Implementation: The Role of Large Type Spaces," Cowles Foundation Discussion Papers 1519, Cowles Foundation for Research in Economics, Yale University.
    11. Guoqiang Tian, 1999. "Bayesian implementation in exchange economies with state dependent preferences and feasible sets," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 16(1), pages 99-119.
    12. Georgy Artemov & Takashi Kunimoto & Roberto Serrano, 2007. "Robust virtual implementation with incomplete information: Towards a reinterpretation of the Wilson doctrine," Working Papers 2007-14, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
    13. Dirk Bergemann & Stephen Morris, 2012. "Ex Post Implementation," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 3, pages 97-152, World Scientific Publishing Co. Pte. Ltd..
    14. Baliga, Sandeep, 1999. "Implementation in Economic Environments with Incomplete Information: The Use of Multi-Stage Games," Games and Economic Behavior, Elsevier, vol. 27(2), pages 173-183, May.
    15. Korpela, Ville & Lombardi, Michele, 2020. "Closure under interim utility equivalence implies two-agent Bayesian implementation," Games and Economic Behavior, Elsevier, vol. 121(C), pages 108-116.
    16. Kunimoto, Takashi & Serrano, Roberto, 2011. "A new necessary condition for implementation in iteratively undominated strategies," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2583-2595.
    17. Tian, Guoqiang, 1997. "Virtual implementation in incomplete information environments with infinite alternatives and types," Journal of Mathematical Economics, Elsevier, vol. 28(3), pages 313-339, October.
    18. Wu, Haoyang, 2011. "Quantum and algorithmic Bayesian mechanisms," MPRA Paper 30072, University Library of Munich, Germany.
    19. Matías Núñez & Carlos Pimienta & Dimitrios Xefteris, 2018. "Implementing the Median," Discussion Papers 2018-11, School of Economics, The University of New South Wales.
    20. Safronov, Mikhail, 2018. "Coalition-proof full efficient implementation," Journal of Economic Theory, Elsevier, vol. 177(C), pages 659-677.

    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

    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:spr:joecth:v:69:y:2020:i:3:d:10.1007_s00199-019-01178-8. 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: Sonal Shukla or Springer Nature Abstracting and Indexing (email available below). General contact details of provider: http://www.springer.com .

    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.