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

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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.

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Bibliographic Info

Paper provided by Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales in its series Working Papers with number 2007-14.

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Date of creation: 27 May 2007
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Handle: RePEc:imd:wpaper:wp2007-14

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Keywords: Wilson doctrine; mechanism design; robust virtual implementation; iteratively undominated strategies; incentive compatibility; measurability; type diversity;

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References

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  1. Eric Maskin & Tomas Sjostrom, 2001. "Implementation Theory," Economics Working Papers 0006, Institute for Advanced Study, School of Social Science.
  2. Dirk Bergemann & Stephen Morris, 2003. "Robust Mechanism Design," Levine's Bibliography 666156000000000035, UCLA Department of Economics.
  3. Roberto Serrano, 2003. "The Theory of Implementation of Social Choice Rules," Economics Working Papers 0033, Institute for Advanced Study, School of Social Science.
  4. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-34, January.
  5. P. Battigalli & M. Siniscalchi, 2002. "Rationalization and Incomplete Information," Princeton Economic Theory Working Papers 9817a118e65062903de7c3577, David K. Levine.
  6. Roberto Serrano & Rajiv Vohra, 2002. "A Characterization of Virtual Bayesian Implementation," Economics Working Papers 0028, Institute for Advanced Study, School of Social Science.
  7. Brandenburger Adam & Dekel Eddie, 1993. "Hierarchies of Beliefs and Common Knowledge," Journal of Economic Theory, Elsevier, vol. 59(1), pages 189-198, February.
  8. 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.
  9. Dirk Bergemann & Stephen Morris, 2005. "Robust Implementation: The Role of Large Type Spaces," Cowles Foundation Discussion Papers 1519, Cowles Foundation for Research in Economics, Yale University.
  10. Philippe Jehiel & Moritz Meyer-ter-Vehn & Benny Moldovanu & William R. Zame, 2005. "The Limits of Ex-Post Implementation," Levine's Bibliography 666156000000000548, UCLA Department of Economics.
  11. 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.
  12. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
  13. Jackson, Matthew O., 1999. "A Crash Course in Implementation Theory," Working Papers 1076, California Institute of Technology, Division of the Humanities and Social Sciences.
  14. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
  15. Chakravorti, Bhaskar, 1992. "Efficiency and Mechanisms with No Regret," International Economic Review, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 45-59, February.
  16. Brandenburger, Adam & Dekel, Eddie, 1987. "Rationalizability and Correlated Equilibria," Econometrica, Econometric Society, vol. 55(6), pages 1391-1402, November.
  17. Palfrey, Thomas R & Srivastava, Sanjay, 1987. "On Bayesian Implementable Allocations," Review of Economic Studies, Wiley Blackwell, vol. 54(2), pages 193-208, April.
  18. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
  19. Serrano, Roberto & Vohra, Rajiv, 2001. "Some Limitations of Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 69(3), pages 785-92, May.
  20. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 65(5), pages 1175-1200, September.
  21. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March.
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Citations

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Cited by:
  1. Dirk Bergemann & Stephen Morris & Olivier Tercieux, 2010. "Rationalizable Implementation," Levine's Working Paper Archive 661465000000000022, David K. Levine.
  2. 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.
  3. Roberto Serrano & Rajiv Vohra, 2009. "Multiplicity of mixed equilibria in mechanisms: A unified approach to exact and approximate implementation," Working Papers 2009-08, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales.
  4. Dirk Bergemann & Stephen Morris, 2009. "Robust Virtual Implementation," Levine's Working Paper Archive 814577000000000155, David K. Levine.
  5. Luis C. Corchon, 2007. "The theory of implementation : what did we learn?," Economics Working Papers we081207, Universidad Carlos III, Departamento de Economía.
  6. Dirk Bergemann & Stephen Morris, 2011. "Robust Mechanism Design: An Introduction," Cowles Foundation Discussion Papers 1818, Cowles Foundation for Research in Economics, Yale University.
  7. Kyungmin Kim & Antonio Penta, 2012. "A Robustly Efficient Auction," Carlo Alberto Notebooks 248, Collegio Carlo Alberto.
  8. Makoto Shimoji & Paul Schweinzer, 2012. "Implementation without Incentive Compatibility: Two Stories with Partially Informed Planners," Discussion Papers 12/21, Department of Economics, University of York.

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