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Maskin meets Abreu and Matsushima

Author

Listed:
  • Chen, Yi-Chun

    (Department of Economics and Risk Management Institute, National University of Singapore)

  • Kunimoto, Takashi

    (Singapore Management University)

  • Sun, Yifei

    (Department of Economics, University of International Business and Economics)

  • Xiong, Siyang

    (Department of Economics, University of California, Riverside)

Abstract

The theory of full implementation has been criticized for using integer/modulo games which admit no equilibrium (Jackson (1992)). To address the critique, we revisit the classical Nash implementation problem due to Maskin (1977, 1999) but allow for the use of lotteries and monetary transfers as in Abreu and Matsushima (1992, 1994). We unify the two well-established but somewhat orthogonal approaches in full implementation theory. We show that Maskin monotonicity is a necessary and sufficient condition for (exact) mixed-strategy Nash implementation by a finite mechanism. In contrast to previous papers, our approach possesses the following features: finite mechanisms (with no integer or modulo game) are used; mixed strategies are handled explicitly; neither undesirable outcomes nor transfers occur in equilibrium; the size of transfers can be made arbitrarily small; and our mechanism is robust to information perturbations.

Suggested Citation

  • Chen, Yi-Chun & Kunimoto, Takashi & Sun, Yifei & Xiong, Siyang, 2022. "Maskin meets Abreu and Matsushima," Theoretical Economics, Econometric Society, vol. 17(4), November.
    • Handle: RePEc:the:publsh:4255
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    References listed on IDEAS

    as
    1. Mariann Ollár & Antonio Penta, 2017. "Full Implementation and Belief Restrictions," American Economic Review, American Economic Association, vol. 107(8), pages 2243-2277, August.
    2. Jihong Lee & Hamid Sabourian, 2011. "Efficient Repeated Implementation," Econometrica, Econometric Society, vol. 79(6), pages 1967-1994, November.
    3. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 66(1), pages 23-38.
    4. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
    5. Matthew O. Jackson, 1992. "Implementation in Undominated Strategies: A Look at Bounded Mechanisms," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(4), pages 757-775.
    6. Philippe Aghion & Drew Fudenberg & Richard Holden & Takashi Kunimoto & Olivier Tercieux, 2012. "Subgame-Perfect Implementation Under Information Perturbations," The Quarterly Journal of Economics, President and Fellows of Harvard College, vol. 127(4), pages 1843-1881.
    7. Jackson Matthew O. & Palfrey Thomas R. & Srivastava Sanjay, 1994. "Undominated Nash Implementation in Bounded Mechanisms," Games and Economic Behavior, Elsevier, vol. 6(3), pages 474-501, May.
    8. Martin J. Osborne & Ariel Rubinstein, 1994. "A Course in Game Theory," MIT Press Books, The MIT Press, edition 1, volume 1, number 0262650401, April.
    9. 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.
    10. Maxwell B. Stinchcombe & Halbert White, 1992. "Some Measurability Results for Extrema of Random Functions Over Random Sets," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 59(3), pages 495-514.
    11. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, vol. 56(5), pages 1191-1220, September.
    12. Dilip Mookherjee & Stefan Reichelstein, 1990. "Implementation via Augmented Revelation Mechanisms," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 57(3), pages 453-475.
    13. Kim-Sau Chung & Jeffrey C. Ely, 2003. "Implementation with Near-Complete Information," Econometrica, Econometric Society, vol. 71(3), pages 857-871, May.
    14. Abreu, Dilip & Matsushima, Hitoshi, 1992. "A Response [Virtual Implementation in Iteratively Undominated Strategies I: Complete Information]," Econometrica, Econometric Society, vol. 60(6), pages 1439-1442, November.
    15. Bhaskar Dutta & Arunava Sen, 1991. "A Necessary and Sufficient Condition for Two-Person Nash Implementation," The Review of Economic Studies, Review of Economic Studies Ltd, vol. 58(1), pages 121-128.
    16. Kunimoto, Takashi, 2019. "Mixed Bayesian implementation in general environments," Journal of Mathematical Economics, Elsevier, vol. 82(C), pages 247-263.
    17. repec:hal:pseose:hal-00812781 is not listed on IDEAS
    18. M. Sanver, 2006. "Nash implementing non-monotonic social choice rules by awards," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(2), pages 453-460, June.
    19. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Jain, Ritesh, 2021. "Rationalizable implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 127(C), pages 47-66.
    2. Takashi Kunimoto & Rene Saran & Roberto Serrano, 2020. "Interim Rationalizable Implementation of Functions," Working Papers 2020-23, Brown University, Department of Economics.
    3. Mukherjee, Saptarshi & Muto, Nozomu & Sen, Arunava, 2024. "Implementation in undominated strategies with applications to auction design, public good provision and matching," Journal of Economic Theory, Elsevier, vol. 216(C).
    4. Soumen Banerjee & Yi-Chun Chen, 2022. "Implementation with Uncertain Evidence," Papers 2209.10741, arXiv.org.
    5. Siyang Xiong, 2022. "Nash implementation by stochastic mechanisms: a simple full characterization," Papers 2211.05431, arXiv.org.
    6. Federico Echenique & Mat'ias N'u~nez, 2022. "Price & Choose," Papers 2212.05650, arXiv.org, revised Apr 2023.

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    More about this item

    Keywords

    Complete information; full implementation; information perturbations; Maskin monotonicity; mixed-strategy Nash equilibrium; social choice function;
    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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