IDEAS home Printed from https://ideas.repec.org/p/ris/smuesw/2020_021.html
   My bibliography  Save this paper

Interim Rationalizable Implementation of Functions

Author

Listed:
  • Kunimoto, Takashi

    (School of Economics, Singapore Management University)

  • Saran, Rene

    (University of Cincinnati)

  • Serrano, Roberto

    (Brown University)

Abstract

This paper investigates rationalizable implementation of social choice functions (SCFs) in incomplete information environments. We identify weak interim rationalizable monotonicity (weak IRM) as a novel condition and show that weak IRM is a necessary and almost sufficient condition for rationalizable implementation. We show by means of an example that interim rationalizable monotonicity (IRM), found in the literature, is strictly stronger than weak IRM as its name suggests, and that IRM is not necessary for rationalizable implementation, as had been previously claimed. The same example also demonstrates that Bayesian monotonicity, the key condition for full Bayesian implementation, is not necessary for rationalizable implementation. This implies that rationalizable implementation can be more permissive than Bayesian implementation: one can exploit the fact that there are no mixed Bayesian equilibria in the implementing mechanism.

Suggested Citation

  • Kunimoto, Takashi & Saran, Rene & Serrano, Roberto, 2020. "Interim Rationalizable Implementation of Functions," Economics and Statistics Working Papers 21-2020, Singapore Management University, School of Economics.
  • Handle: RePEc:ris:smuesw:2020_021
    as

    Download full text from publisher

    File URL: https://ink.library.smu.edu.sg/soe_research/2406/
    File Function: Full text
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-134, January.
    2. 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..
    3. Dirk Bergemann & Stephen Morris, 2012. "Robust Virtual Implementation," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 8, pages 263-317, World Scientific Publishing Co. Pte. Ltd..
    4. Marion Oury & Olivier Tercieux, 2012. "Continuous Implementation," PSE-Ecole d'économie de Paris (Postprint) halshs-00754580, HAL.
    5. Chen, Yi-Chun & Kunimoto, Takashi & Sun, Yifei & Xiong, Siyang, 2021. "Rationalizable implementation in finite mechanisms," Games and Economic Behavior, Elsevier, vol. 129(C), pages 181-197.
    6. Battigalli Pierpaolo & Siniscalchi Marciano, 2003. "Rationalization and Incomplete Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 3(1), pages 1-46, June.
    7. Eric Maskin, 1999. "Nash Equilibrium and Welfare Optimality," Review of Economic Studies, Oxford University Press, vol. 66(1), pages 23-38.
    8. Adam Brandenburger & Eddie Dekel, 2014. "Rationalizability and Correlated Equilibria," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 3, pages 43-57, World Scientific Publishing Co. Pte. Ltd..
    9. Mezzetti, Claudio & Renou, Ludovic, 2012. "Implementation in mixed Nash equilibrium," Journal of Economic Theory, Elsevier, vol. 147(6), pages 2357-2375.
    10. Jain, Ritesh, 2021. "Rationalizable implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 127(C), pages 47-66.
    11. Bernheim, B Douglas, 1984. "Rationalizable Strategic Behavior," Econometrica, Econometric Society, vol. 52(4), pages 1007-1028, July.
    12. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-477, March.
    13. Serrano, Roberto & Vohra, Rajiv, 2005. "A characterization of virtual Bayesian implementation," Games and Economic Behavior, Elsevier, vol. 50(2), pages 312-331, February.
    14. , & , & ,, 2007. "Interim correlated rationalizability," Theoretical Economics, Econometric Society, vol. 2(1), pages 15-40, March.
    15. Takashi Kunimoto & Roberto Serrano, 2019. "Rationalizable Implementation of Correspondences," Management Science, INFORMS, vol. 44(4), pages 1326-1344, November.
    16. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
    17. Serrano, Roberto & Vohra, Rajiv, 2001. "Some Limitations of Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 69(3), pages 785-792, May.
    18. 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.
    19. Marion Oury & Olivier Tercieux, 2012. "Continuous Implementation," Econometrica, Econometric Society, vol. 80(4), pages 1605-1637, July.
    20. Battigalli Pierpaolo & Di Tillio Alfredo & Grillo Edoardo & Penta Antonio, 2011. "Interactive Epistemology and Solution Concepts for Games with Asymmetric Information," The B.E. Journal of Theoretical Economics, De Gruyter, vol. 11(1), pages 1-40, March.
    21. Chen, Yi-Chun & Kunimoto, Takashi & Sun, Yifei & Xiong, Siyang, 2022. "Maskin meets Abreu and Matsushima," Theoretical Economics, Econometric Society, vol. 17(4), November.
    22. Kunimoto, Takashi & Saran, Rene, 2020. "Robust Implementation in Rationalizable Strategies in General Mechanisms," Economics and Statistics Working Papers 10-2020, Singapore Management University, School of Economics.
    23. Di Tillio, Alfredo, 2011. "A robustness result for rationalizable implementation," Games and Economic Behavior, Elsevier, vol. 72(1), pages 301-305, May.
    24. Artemov, Georgy & Kunimoto, Takashi & Serrano, Roberto, 2013. "Robust virtual implementation: Toward a reinterpretation of the Wilson doctrine," Journal of Economic Theory, Elsevier, vol. 148(2), pages 424-447.
    25. 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.
    26. Pearce, David G, 1984. "Rationalizable Strategic Behavior and the Problem of Perfection," Econometrica, Econometric Society, vol. 52(4), pages 1029-1050, July.
    27. Lipman Barton L., 1994. "A Note on the Implications of Common Knowledge of Rationality," Games and Economic Behavior, Elsevier, vol. 6(1), pages 114-129, January.
    28. Kunimoto, Takashi, 2019. "Mixed Bayesian implementation in general environments," Journal of Mathematical Economics, Elsevier, vol. 82(C), pages 247-263.
    29. Battigalli, Pierpaolo, 2003. "Rationalizability in infinite, dynamic games with incomplete information," Research in Economics, Elsevier, vol. 57(1), pages 1-38, March.
    30. 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)

    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. Victor H. Aguiar & Per Hjertstrand & Roberto Serrano, 2020. "Rationalizable Incentives: Interim Implementation of Sets in Rationalizable Strategies," Working Papers 2020-16, 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. 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..
    4. Jain, Ritesh, 2021. "Rationalizable implementation of social choice correspondences," Games and Economic Behavior, Elsevier, vol. 127(C), pages 47-66.
    5. Shimoji, Makoto & Schweinzer, Paul, 2015. "Implementation without incentive compatibility: Two stories with partially informed planners," Games and Economic Behavior, Elsevier, vol. 91(C), pages 258-267.
    6. Dirk Bergemann & Stephen Morris, 2012. "Robust Implementation in General Mechanisms," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 5, pages 195-239, World Scientific Publishing Co. Pte. Ltd..
    7. Kunimoto, Takashi, 2020. "Robust virtual implementation with almost complete information," Mathematical Social Sciences, Elsevier, vol. 108(C), pages 62-73.
    8. 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.
    9. Dirk Bergemann & Stephen Morris, 2012. "Robust Implementation in Direct Mechanisms," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 4, pages 153-194, World Scientific Publishing Co. Pte. Ltd..
    10. Müller, Christoph, 2016. "Robust virtual implementation under common strong belief in rationality," Journal of Economic Theory, Elsevier, vol. 162(C), pages 407-450.
    11. Chen, Yi-Chun & Kunimoto, Takashi & Sun, Yifei & Xiong, Siyang, 2021. "Rationalizable implementation in finite mechanisms," Games and Economic Behavior, Elsevier, vol. 129(C), pages 181-197.
    12. Takashi Kunimoto & Roberto Serrano, 2019. "Rationalizable Implementation of Correspondences," Management Science, INFORMS, vol. 44(4), pages 1326-1344, November.
    13. Bergemann, Dirk & Morris, Stephen & Takahashi, Satoru, 2017. "Interdependent preferences and strategic distinguishability," Journal of Economic Theory, Elsevier, vol. 168(C), pages 329-371.
    14. Artemov, Georgy & Kunimoto, Takashi & Serrano, Roberto, 2013. "Robust virtual implementation: Toward a reinterpretation of the Wilson doctrine," Journal of Economic Theory, Elsevier, vol. 148(2), pages 424-447.
    15. Georgy Artemov & Takashi Kunimoto & Roberto Serrano, 2007. "Robust virtual implementation with incomplete information: Towards a reinterpretation of the Wilson doctrine," Working Papers 2007-14, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
    16. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Working Papers 2003-19, Brown University, Department of Economics.
    17. Müller, Christoph, 2020. "Robust implementation in weakly perfect Bayesian strategies," Journal of Economic Theory, Elsevier, vol. 189(C).
    18. 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.
    19. Kunimoto, Takashi & Serrano, Roberto, 2011. "A new necessary condition for implementation in iteratively undominated strategies," Journal of Economic Theory, Elsevier, vol. 146(6), pages 2583-2595.
    20. 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.

    More about this item

    Keywords

    Bayesian incentive compatibility; bayesian monotonicity; weak interim rationalizable monotonicity; interim rationalizable monotonicity; implementation; rationalizability;
    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

    NEP fields

    This paper has been announced in the following NEP Reports:

    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:ris:smuesw:2020_021. See general information about how to correct material in RePEc.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: . General contact details of provider: https://edirc.repec.org/data/sesmusg.html .

    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: Cheong Pei Qi The email address of this maintainer does not seem to be valid anymore. Please ask Cheong Pei Qi to update the entry or send us the correct address (email available below). General contact details of provider: https://edirc.repec.org/data/sesmusg.html .

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

    IDEAS is a RePEc service hosted by the Research Division of the Federal Reserve Bank of St. Louis . RePEc uses bibliographic data supplied by the respective publishers.