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On amending the sufficient conditions for Nash implementation

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  • Wu, Haoyang

Abstract

Mechanism design, a reverse problem of game theory, is an important branch of economics. Nash implementation is the cornerstone of the theory of mechanism design. The well-known Maskin's theorem describes the sufficient conditions for Nash implementation when the number of agents are at least three. A recent work [H. Wu, Quantum mechanism helps agents combat ``bad'' social choice rules. International Journal of Quantum Information, 2010 (accepted) http://arxiv.org/abs/1002.4294 ] shows that when an additional condition is satisfied, the Maskin's theorem will no longer hold by using a quantum mechanism. Although quantum mechanisms are theoretically feasible, agents cannot benefit from them immediately due to the restriction of current experimental technologies. In this paper, we will go beyond the obstacle of how to realize quantum mechanisms, and propose an algorithmic mechanism which leads to the same results as quantum mechanisms do. Consequently, the sufficent conditions for Nash implementation are amended not only in the quantum world, but also in the real world.

Suggested Citation

  • Wu, Haoyang, 2011. "On amending the sufficient conditions for Nash implementation," MPRA Paper 30067, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:30067
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    References listed on IDEAS

    as
    1. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    2. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Working Papers 2003-19, Brown University, Department of Economics.
    3. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Working Papers 2003-19, Brown University, Department of Economics.
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    Cited by:

    1. Wu, Haoyang, 2011. "A novel result on the revenue equivalence theorem," MPRA Paper 31988, University Library of Munich, Germany.
    2. Wu, Haoyang, 2011. "Two-agent Nash implementation: A new result," MPRA Paper 30068, University Library of Munich, Germany.
    3. Wu, Haoyang, 2011. "Quantum Bayesian implementation and revelation principle," MPRA Paper 30653, University Library of Munich, Germany.
    4. Wu, Haoyang, 2011. "Subgame perfect implementation: A new result," MPRA Paper 30286, University Library of Munich, Germany.
    5. Wu, Haoyang, 2011. "Quantum and algorithmic Bayesian mechanisms," MPRA Paper 30072, University Library of Munich, Germany.

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    More about this item

    Keywords

    Quantum computing; Mechanism design; Nash implementation;
    All these keywords.

    JEL classification:

    • D71 - Microeconomics - - Analysis of Collective Decision-Making - - - Social Choice; Clubs; Committees; Associations

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