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The Theory of Implementation of Social Choice Rules

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  • Roberto Serrano

    (Department of Economics, Brown University)

Abstract

Suppose that the goals of a society can be summarized in a social choice rule, i.e., a mapping from relevant underlying parameters to final outcomes. Typically, the underlying parameters (e.g., individual preferences) are private information to the agents in society. The implementation problem is then formulated: under what circumstances can one design a mechanism so that the private information is truthfully elicited and the social optimum ends up being implemented? In designing such a mechanism, appropriate incentives will have to be given to the agents so that they do not wish to misrepresent their information. The theory of implementation or mechanism design formalizes this “social engineering” problem and provides answers to the question just posed. I survey the theory of implementation in this article, emphasizing the results based on two behavioral assumptions for the agents (dominant strategies and Nash equilibrium). Examples discussed include voting, and the allocation of private and public goods under complete and incomplete information.

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  • Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Economics Working Papers 0033, Institute for Advanced Study, School of Social Science.
    • Handle: RePEc:ads:wpaper:0033
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    Cited by:

    1. Axel Ockenfels, 2009. "Marktdesign und Experimentelle Wirtschaftsforschung," Perspektiven der Wirtschaftspolitik, Verein für Socialpolitik, vol. 10(s1), pages 31-53, May.
    2. 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.
    3. Antonio Cabrales & Roberto Serrano, 2007. "Implemetation in Adaptive Better-Response Dynamics," Working Papers wp2007_0708, CEMFI.
    4. Eric S. Maskin, 2008. "Mechanism Design: How to Implement Social Goals," American Economic Review, American Economic Association, vol. 98(3), pages 567-576, June.
    5. Anirban Kar & Indrajit Ray & Roberto Serrano, 2005. "Multiple Equilibria as a Difficulty in Understanding Correlated Distributions," Working Papers 2005-10, Brown University, Department of Economics.
    6. Tumennasan, Norovsambuu, 2013. "To err is human: Implementation in quantal response equilibria," Games and Economic Behavior, Elsevier, vol. 77(1), pages 138-152.
    7. Roberto Serrano, 2004. "Fifty Years of the Nash Program, 1953-2003," Working Papers 2004-20, Brown University, Department of Economics.
    8. Wu, Haoyang, 2011. "A novel result on the revenue equivalence theorem," MPRA Paper 31988, University Library of Munich, Germany.
    9. Wu, Haoyang, 2011. "Quantum Bayesian implementation and revelation principle," MPRA Paper 30653, University Library of Munich, Germany.
    10. Roberto Serrano & Antonio Cabrales, 2007. "Implementation in Adaptive Better-Response Dynamics," Working Papers 2007-10, Brown University, Department of Economics.
    11. Eric Maskin, 2004. "The Unity of Auction Theory: Paul Milgrom's Masterclass," Economics Working Papers 0044, Institute for Advanced Study, School of Social Science.
    12. Corchón, Luis C., 2008. "The theory of implementation : what did we learn?," UC3M Working papers. Economics we081207, Universidad Carlos III de Madrid. Departamento de Economía.
    13. Wu, Haoyang, 2011. "Quantum and algorithmic Bayesian mechanisms," MPRA Paper 30072, University Library of Munich, Germany.
    14. Roberto Serrano, 2005. "Fifty years of the Nash program, 1953-2003," Investigaciones Economicas, Fundación SEPI, vol. 29(2), pages 219-258, May.
    15. Georgy Artemov & Takashi Kunimoto & Roberto Serrano, 2007. "Robust Virtual Implementation with Incomplete Information: Toward a Reinterpretation of the Wilson Doctrine," Working Papers 2007-6, Brown University, Department of Economics.
    16. Wu, Haoyang, 2011. "On amending the sufficient conditions for Nash implementation," MPRA Paper 30067, University Library of Munich, Germany.

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    More about this item

    Keywords

    Implementation Theory; Mechanism Design; Asymmetric Information; Decentralization; Game Theory; Dominance; Nash Equilibrium; Monotonicity;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • D78 - Microeconomics - - Analysis of Collective Decision-Making - - - Positive Analysis of Policy Formulation and Implementation
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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