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Robust virtual implementation: Toward a reinterpretation of the Wilson doctrine

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  • Artemov, Georgy
  • Kunimoto, Takashi
  • Serrano, Roberto

Abstract

We study a mechanism design problem where arbitrary restrictions are placed on the sets of first-order beliefs of agents. Calling these restrictions Δ, we use Δ-rationalizability (Battigalli and Siniscalchi, 2003, [5]) as our solution concept, and require that a mechanism virtually implement a socially desirable outcome. We obtain two necessary conditions, Δ-incentive compatibility and Δ-measurability and show that the latter is satisfied as long as a particular zero-measure set of first-order beliefs is ruled out. In environments allowing small transfers of utility among agents, these two conditions are also sufficient.

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Bibliographic Info

Article provided by Elsevier in its journal Journal of Economic Theory.

Volume (Year): 148 (2013)
Issue (Month): 2 ()
Pages: 424-447

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Handle: RePEc:eee:jetheo:v:148:y:2013:i:2:p:424-447

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Web page: http://www.elsevier.com/locate/inca/622869

Related research

Keywords: Wilson doctrine; Mechanism design; Robust virtual implementation; Δ-rationalizability; Incentive compatibility; Measurability; Type diversity;

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References

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  1. 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, 05.
  2. Dirk Bergemann & Stephen Morris, 2009. "Robust Virtual Implementation," Levine's Working Paper Archive 814577000000000155, David K. Levine.
  3. Sjostrom, Tomas & Yamato, Takehiko & Saijo, Tatsuyoshi, 2007. "Secure implementation," Theoretical Economics, Econometric Society, vol. 2(3), September.
  4. Bergemann, Dirk & Morris, Stephen, 2011. "Robust implementation in general mechanisms," Games and Economic Behavior, Elsevier, vol. 71(2), pages 261-281, March.
  5. Serrano, Roberto & Vohra, Rajiv, 2005. "A characterization of virtual Bayesian implementation," Games and Economic Behavior, Elsevier, vol. 50(2), pages 312-331, February.
  6. Jackson, Matthew O., 1999. "A Crash Course in Implementation Theory," Working Papers 1076, California Institute of Technology, Division of the Humanities and Social Sciences.
  7. Morris, Stephen & Dekel, Eddie & Fudenberg, Drew, 2007. "Interim Correlated Rationalizability," Scholarly Articles 3196333, Harvard University Department of Economics.
  8. Zvika Neeman, 1998. "The Relevance of Private Information in Mechanism Design," Papers 0093, Boston University - Industry Studies Programme.
  9. Takashi Kunimoto & Roberto Serrano, 2010. "A New Necessary Condition for Implementation in Iteratively Undominated Strategies," Working Papers 2010-2, Brown University, Department of Economics.
  10. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June.
  11. Cremer, Jacques & McLean, Richard P, 1988. "Full Extraction of the Surplus in Bayesian and Dominant Strategy Auctions," Econometrica, Econometric Society, vol. 56(6), pages 1247-57, November.
  12. 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.
  13. Aviad Heifetz & Zvika Neeman, 2004. "On the Generic (Im)possibility of Full Surplus Extraction in Mechanism Design," Discussion Paper Series dp350, The Center for the Study of Rationality, Hebrew University, Jerusalem.
  14. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
  15. Pierpaolo Battigalli & Alfredo Di Tillio & Edoardo Grillo & Antonio Penta, 2008. "Interactive Epistemology and Solution Concepts for Games with Asymmetric Information," Working Papers 340, IGIER (Innocenzo Gasparini Institute for Economic Research), Bocconi University.
  16. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 65(5), pages 1175-1200, September.
  17. Abreu, Dilip & Matsushima, Hitoshi, 1992. "A Response [Virtual Implementation in Iteratively Undominated Strategies I: Complete Information]," Econometrica, Econometric Society, vol. 60(6), pages 1439-42, November.
  18. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
  19. Serrano, Roberto & Vohra, Rajiv, 2001. "Some Limitations of Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 69(3), pages 785-92, May.
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Cited by:
  1. Pivato, Marcus, 2013. "Statistical utilitarianism," MPRA Paper 49561, University Library of Munich, Germany.

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