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A Full Characterization of Nash Implementation with Strategy Space Reduction

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  • Lombardi, Michele
  • Yoshihara, Naoki
  • 吉原, 直毅
  • ヨシハラ, ナオキ

Abstract

Noting that a full characterization of Nash-implementation is given using a canonical-mechanism and Maskin’s theorem (Maskin, 1999) is shown using a mechanism with Saijo’s type of strategy space reduction (Saijo, 1988), this paper fully characterizes the class of Nashimplementable social choice correspondences (SCCs) by mechanisms endowed with Saijo’s message space specification - s-mechanisms. This class of SCCs is further shown to be equivalent to the class of Nashimplementable SCCs, though any further ‘strategy space reduction’ mechanism breaks this equivalent relationship down.

Suggested Citation

  • Lombardi, Michele & Yoshihara, Naoki & 吉原, 直毅 & ヨシハラ, ナオキ, 2011. "A Full Characterization of Nash Implementation with Strategy Space Reduction," Discussion Paper Series a548, Institute of Economic Research, Hitotsubashi University.
    • Handle: RePEc:hit:hituec:a548
    Note: 40561
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    Cited by:

    1. Michele Lombardi & Naoki Yoshihara, 2020. "Partially-honest Nash implementation: a full characterization," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 70(3), pages 871-904, October.
    2. Lombardi, Michele & Yoshihara, Naoki, 2016. "Partially-honest Nash Implementation with Non-connected Honesty Standards," Discussion Paper Series 633, Institute of Economic Research, Hitotsubashi University.
    3. Lombardi, Michele, 2010. "Two-agent Nash implementation with partially-honest agents: Almost Full Characterizations," MPRA Paper 27834, University Library of Munich, Germany.
    4. Korpela, Ville & Lombardi, Michele & Vartiainen, Hannu, 2020. "Do coalitions matter in designing institutions?," Journal of Economic Theory, Elsevier, vol. 185(C).
    5. R Jain & V Korpela & M Lombardi, 2022. "Two-Player Rationalizable Implementation," Working Papers 202228, University of Liverpool, Department of Economics.
    6. Jens Leth Hougaard & Mich Tvede, 2020. "Implementation of Optimal Connection Networks," IFRO Working Paper 2020/06, University of Copenhagen, Department of Food and Resource Economics.
    7. Lombardi, M. & Yoshihara, N., 2018. "Treading a fine line: (Im)possibilities for Nash implementation with partially-honest individuals," Games and Economic Behavior, Elsevier, vol. 111(C), pages 203-216.
    8. Hayashi, Takashi & Lombardi, Michele, 2019. "One-step-ahead implementation," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 110-126.
    9. Hayashi, Takashi & Lombardi, Michele, 2019. "Constrained implementation," Journal of Economic Theory, Elsevier, vol. 183(C), pages 546-567.
    10. Lombardi, Michele & Yoshihara, Naoki, 2013. "Natural implementation with partially honest agents in economic environments," MPRA Paper 48294, University Library of Munich, Germany.
    11. Lombardi, Michele & Yoshihara, Naoki, 2011. "Partially-honest Nash implementation: Characterization results," MPRA Paper 28838, University Library of Munich, Germany.
    12. Naoki Yoshihara & Akira Yamada, 2019. "Nash implementation in production economies with unequal skills: a characterization," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 53(1), pages 113-134, June.
    13. Michele Lombardi & Naoki Yoshihara, 2017. "Treading a Â…fine line: (Im)possibilities for Nash implementation with partially-honest individuals," Working Papers SDES-2017-14, Kochi University of Technology, School of Economics and Management, revised Aug 2017.
    14. Lombardi, Michele & Yoshihara, Naoki, 2012. "Natural Implementation with Partially Honest Agents," Discussion Paper Series 561, Institute of Economic Research, Hitotsubashi University.
    15. Lombardi, Michele & Yoshihara, Naoki, 2014. "Natural Implementation with Partially-honest Agents in Economic Environments with Free-disposal," Discussion Paper Series 616, Institute of Economic Research, Hitotsubashi University.
    16. Huiyi Guo & Nicholas C. Yannelis, 2022. "Incentive compatibility under ambiguity," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 73(2), pages 565-593, April.
    17. Hayashi, Takashi & Lombardi, Michele, 2017. "Implementation in partial equilibrium," Journal of Economic Theory, Elsevier, vol. 169(C), pages 13-34.
    18. 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.
    19. Jianxin Yi, 2021. "Nash implementation via mechanisms that allow for abstentions," Theory and Decision, Springer, vol. 91(2), pages 279-288, September.
    20. Lombardi, M. & Yoshihara, N., 2012. "National implementation with partially honest agents," Research Memorandum 005, Maastricht University, Maastricht Research School of Economics of Technology and Organization (METEOR).

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    More about this item

    Keywords

    Nash implementation; strategy space reduction; s-mechanisms; Condition μsr; Condition Ms;
    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
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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