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Nash implementation via simple stochastic mechanisms: strategy space reduction

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  • Michele Lombardi

Abstract

Benoît and Ok (Games Econ Behav 64:51–67, 2008 ) show that in a society with at least three agents any weakly unanimous social choice correspondence (SCC) is Maskin’s monotonic if and only if it is Nash-implementable via a simple stochastic mechanism (Benoît-Ok’s Theorem). This paper fully identifies the class of weakly unanimous SCCs that are Nash-implementable via a simple stochastic mechanism endowed with Saijo’s message space specification (Saijo in Econometrica 56:693–700, 1988 ). It is shown that this class of SCCs is equivalent to the class of SCCs that are Nash-implementable via Benoît-Ok’s Theorem. Copyright The Author(s) 2012

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  • Michele Lombardi, 2012. "Nash implementation via simple stochastic mechanisms: strategy space reduction," Review of Economic Design, Springer;Society for Economic Design, vol. 16(4), pages 297-309, December.
    • Handle: RePEc:spr:reecde:v:16:y:2012:i:4:p:297-309
    DOI: 10.1007/s10058-012-0117-7
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    References listed on IDEAS

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    1. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
    2. 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.
    3. Michele Lombardi & Naoki Yoshihara, 2013. "A full characterization of nash implementation with strategy space reduction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 131-151, September.
    4. Yamato, Takehiko, 1992. "On nash implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 4(3), pages 484-492, July.
    5. Danilov, Vladimir, 1992. "Implementation via Nash Equilibria," Econometrica, Econometric Society, vol. 60(1), pages 43-56, January.
    6. Saijo, Tatsuyoshi, 1988. "Strategy Space Reduction in Maskin's Theorem: Sufficient Conditions for Nash Implementation," Econometrica, Econometric Society, vol. 56(3), pages 693-700, May.
    7. Lombardi, Michele & Yoshihara, Naoki & 吉原, 直毅, 2011. "Partially-honest Nash implementation: Characterization results," CCES Discussion Paper Series 43, Center for Research on Contemporary Economic Systems, Graduate School of Economics, Hitotsubashi University.
    8. Moore, John & Repullo, Rafael, 1990. "Nash Implementation: A Full Characterization," Econometrica, Econometric Society, vol. 58(5), pages 1083-1099, September.
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    Citations

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    Cited by:

    1. Azacis, Helmuts & Vida, Péter, 2015. "Repeated Implementation," Discussion Paper Series of SFB/TR 15 Governance and the Efficiency of Economic Systems 518, Free University of Berlin, Humboldt University of Berlin, University of Bonn, University of Mannheim, University of Munich.
    2. Michele Lombardi & Naoki Yoshihara, 2013. "A full characterization of nash implementation with strategy space reduction," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 54(1), pages 131-151, September.
    3. Jianxin Yi, 2021. "Nash implementation via mechanisms that allow for abstentions," Theory and Decision, Springer, vol. 91(2), pages 279-288, September.

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    More about this item

    Keywords

    Nash implementation; Strategy space reduction; Informational efficiency; Simple stochastic mechanisms; C72; D71;
    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

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