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Robust virtual implementation with incomplete information: Towards a reinterpretation of the Wilson doctrine

Author

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  • Georgy Artemov

    (Brown University)

  • Takashi Kunimoto

    (McGill University)

  • Roberto Serrano

    (Brown University and IMDEA Social Sciences)

Abstract

We consider robust virtual implementation, where robustness is the requirement that implementation succeed in all type spaces consistent with a given payoff type space as well as with a given space of first-order beliefs about the other agents\' payoff types. This last bit, which constitutes our reinterpretation of the Wilson doctrine, allows us to obtain very permissive results. Our first result is that generically, if there are at least three alternatives, any incentive compatible social choice function is robustly virtually implementable in iteratively undominated strategies. Further, we characterize robust virtual implementation in iteratively undominated strategies by means of incentive compatibility and measurability. Our characterization is independent of the presence of monetary transfers or assumptions alike, made in previous studies. Our work also clarifies the measurability condition in connection to the generic diversity of preferences used in our first result.

Suggested Citation

  • 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.
  • Handle: RePEc:imd:wpaper:wp2007-14
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    References listed on IDEAS

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    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, 2005. "Robust Implementation: The Role of Large Type Spaces," Levine's Bibliography 784828000000000116, UCLA Department of Economics.
    3. Adam Brandenburger & Eddie Dekel, 2014. "Hierarchies of Beliefs and Common Knowledge," World Scientific Book Chapters, in: The Language of Game Theory Putting Epistemics into the Mathematics of Games, chapter 2, pages 31-41, World Scientific Publishing Co. Pte. Ltd..
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    6. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 2, pages 49-96, World Scientific Publishing Co. Pte. Ltd..
    7. 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.
    8. MERTENS, Jean-François & ZAMIR, Shmuel, 1985. "Formulation of Bayesian analysis for games with incomplete information," LIDAM Reprints CORE 608, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    9. 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..
    10. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-477, March.
    11. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 65(5), pages 1175-1200, September.
    12. Dirk Bergemann & Stephen Morris, 2007. "Strategic Distinguishability with an Application to Robust Virtual Implementation," Cowles Foundation Discussion Papers 1609, Cowles Foundation for Research in Economics, Yale University.
    13. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
    14. Palfrey, Thomas R., 2002. "Implementation theory," Handbook of Game Theory with Economic Applications, in: R.J. Aumann & S. Hart (ed.), Handbook of Game Theory with Economic Applications, edition 1, volume 3, chapter 61, pages 2271-2326, Elsevier.
    15. Serrano, Roberto & Vohra, Rajiv, 2005. "A characterization of virtual Bayesian implementation," Games and Economic Behavior, Elsevier, vol. 50(2), pages 312-331, February.
    16. Philippe Jehiel & Moritz Meyer-ter-Vehn & Benny Moldovanu & William R. Zame, 2006. "The Limits of ex post Implementation," Econometrica, Econometric Society, vol. 74(3), pages 585-610, May.
    17. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Economics Working Papers 0033, Institute for Advanced Study, School of Social Science.
    18. 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.
    19. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
    20. 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.
    21. Serrano, Roberto & Vohra, Rajiv, 2001. "Some Limitations of Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 69(3), pages 785-792, May.
    22. 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. 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..
    2. Mariann Ollar & Antonio Penta, 2021. "A network solution to robust implementation: The case of identical but unknown distributions," Economics Working Papers 1776, Department of Economics and Business, Universitat Pompeu Fabra.
    3. 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.
    4. 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..
    5. Chen, Jing & Micali, Silvio, 2015. "Mechanism design with possibilistic beliefs," Journal of Economic Theory, Elsevier, vol. 156(C), pages 77-102.
    6. Mariann Ollár & Antonio Penta, 2019. "Implementation via transfers with identical but unknown distributions," Economics Working Papers 1676, Department of Economics and Business, Universitat Pompeu Fabra.
    7. 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.
    8. Kyungmin Kim & Antonio Penta, 2012. "A Robustly Efficient Auction," Carlo Alberto Notebooks 248, Collegio Carlo Alberto.
    9. Dirk Bergemann & Stephen Morris, 2012. "Robust Mechanism Design: An Introduction," World Scientific Book Chapters, in: Robust Mechanism Design The Role of Private Information and Higher Order Beliefs, chapter 1, pages 1-48, World Scientific Publishing Co. Pte. Ltd..
    10. 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.
    11. Takashi Kunimoto & Roberto Serrano, 2010. "Evaluating the Conditions for Robust Mechanism Design Abstract: We assess the strength of the different conditions identified in the literature of robust mechanism design. We focus on three conditions," Working Papers 2010-6, Brown University, Department of Economics.
    12. Corchón, Luis C., 2008. "The theory of implementation : what did we learn?," UC3M Working papers. Economics we081207, Universidad Carlos III de Madrid. Departamento de Economía.
    13. Di Tillio, Alfredo, 2011. "A robustness result for rationalizable implementation," Games and Economic Behavior, Elsevier, vol. 72(1), pages 301-305, May.

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    More about this item

    Keywords

    Wilson doctrine; mechanism design; robust virtual implementation; iteratively undominated strategies; incentive compatibility; measurability; type diversity;
    All these keywords.

    JEL classification:

    • C72 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Noncooperative Games
    • C78 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Bargaining Theory; Matching Theory
    • D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information; Mechanism Design

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