IDEAS home Printed from https://ideas.repec.org/a/the/publsh/4255.html
   My bibliography  Save this article

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
    as

    Download full text from publisher

    File URL: http://econtheory.org/ojs/index.php/te/article/viewFile/20221683/35309/1042
    Download Restriction: no
    ---><---

    Other versions of this item:

    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, December.
    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. 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.
    18. 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

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    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. Soumen Banerjee & Yi-Chun Chen, 2022. "Implementation with Uncertain Evidence," Papers 2209.10741, arXiv.org.
    4. Siyang Xiong, 2022. "Nash implementation by stochastic mechanisms: a simple full characterization," Papers 2211.05431, arXiv.org.
    5. Federico Echenique & Mat'ias N'u~nez, 2022. "Price & Choose," Papers 2212.05650, arXiv.org, revised Apr 2023.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Working Papers 2003-19, Brown University, Department of Economics.
    2. Jain, Ritesh & Lombardi, Michele, 2022. "Continuous virtual implementation: Complete information," Journal of Mathematical Economics, Elsevier, vol. 99(C).
    3. Maskin, Eric & Sjostrom, Tomas, 2002. "Implementation theory," Handbook of Social Choice and Welfare,in: K. J. Arrow & A. K. Sen & K. Suzumura (ed.), Handbook of Social Choice and Welfare, edition 1, volume 1, chapter 5, pages 237-288 Elsevier.
    4. Kartik, Navin & Tercieux, Olivier & Holden, Richard, 2014. "Simple mechanisms and preferences for honesty," Games and Economic Behavior, Elsevier, vol. 83(C), pages 284-290.
    5. Lee, Jihong & Sabourian, Hamid, 2015. "Complexity and repeated implementation," Journal of Economic Theory, Elsevier, vol. 158(PA), pages 259-292.
    6. Chen, Yi-Chun & Sun, Yifei, 2015. "Full implementation in backward induction," Journal of Mathematical Economics, Elsevier, vol. 59(C), pages 71-76.
    7. Matthew O. Jackson, 2001. "A crash course in implementation theory," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 18(4), pages 655-708.
    8. Hayashi, Takashi & Lombardi, Michele, 2019. "One-step-ahead implementation," Journal of Mathematical Economics, Elsevier, vol. 83(C), pages 110-126.
    9. Ortner, Juan, 2015. "Direct implementation with minimally honest individuals," Games and Economic Behavior, Elsevier, vol. 90(C), pages 1-16.
    10. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
    11. 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.
    12. Takahashi, Satoru & Tercieux, Olivier, 2020. "Robust equilibrium outcomes in sequential games under almost common certainty of payoffs," Journal of Economic Theory, Elsevier, vol. 188(C).
    13. Hayashi, Takashi & Lombardi, Michele, 2019. "Constrained implementation," Journal of Economic Theory, Elsevier, vol. 183(C), pages 546-567.
    14. Dirk Bergemann & Stephen Morris & Olivier Tercieux, 2012. "Rationalizable Implementation," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 11, pages 375-404, World Scientific Publishing Co. Pte. Ltd..
    15. Hitoshi Matsushima, 2021. "Partial ex-post verifiability and unique implementation of social choice functions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 56(3), pages 549-567, April.
    16. Korpela, Ville & Lombardi, Michele & Vartiainen, Hannu, 2020. "Do coalitions matter in designing institutions?," Journal of Economic Theory, Elsevier, vol. 185(C).
    17. Cabrales, Antonio & Serrano, Roberto, 2011. "Implementation in adaptive better-response dynamics: Towards a general theory of bounded rationality in mechanisms," Games and Economic Behavior, Elsevier, vol. 73(2), pages 360-374.
    18. Roberto Serrano & Rajiv Vohra, 2009. "Multiplicity of Mixed Equilibria in Mechanisms: a Unified Approach ot Exact and Approximate Implementation," Working Papers 2009-11, Brown University, Department of Economics.
    19. Jing Chen & Silvio Micali, 2016. "Leveraging Possibilistic Beliefs in Unrestricted Combinatorial Auctions," Games, MDPI, vol. 7(4), pages 1-19, October.
    20. Caffera, Marcelo & Dubra, Juan & Figueroa, Nicolás, 2018. "Mechanism design when players’ preferences and information coincide," Mathematical Social Sciences, Elsevier, vol. 91(C), pages 56-61.

    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

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:the:publsh:4255. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Martin J. Osborne (email available below). General contact details of provider: http://econtheory.org .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.