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Robust virtual implementation: Toward a reinterpretation of the Wilson doctrine

Author Info

  • 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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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
Contact details of provider: Web page: http://www.elsevier.com/locate/inca/622869

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

Find related papers by 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

References listed on IDEAS
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  1. Aviad Heifetz & Zvika Neeman, 2006. "On the Generic (Im)Possibility of Full Surplus Extraction in Mechanism Design," Econometrica, Econometric Society, vol. 74(1), pages 213-233, 01.
  2. 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.
  3. 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.
  4. Eddie Dekel & Drew Fudenberg & Stephen Morris, 2006. "Interim Correlated Rationalizability," Levine's Bibliography 122247000000001188, UCLA Department of Economics.
  5. Bergemann, Dirk & Morris, Stephen, 2009. "Robust virtual implementation," Theoretical Economics, Econometric Society, vol. 4(1), March.
  6. 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.
  7. 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.
  8. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 65(5), pages 1175-1200, September.
  9. Neeman, Z., 1998. "The Relevance of Private Infromation in Mechanism Design," Papers 93, Boston University - Department of Economics.
  10. Bergemann, Dirk & Morris, Stephen, 2011. "Robust implementation in general mechanisms," Games and Economic Behavior, Elsevier, vol. 71(2), pages 261-281, March.
  11. 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.
  12. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June.
  13. 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.
  14. Tatsuyoshi Saijo & Tomas Sjöström & Takehiko Yamato, 2004. "Secure Implementation," Levine's Bibliography 122247000000000615, UCLA Department of Economics.
  15. 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.
  16. Roberto Serrano & Rajiv Vohra, 2002. "A Characterization of Virtual Bayesian Implementation," Economics Working Papers 0028, Institute for Advanced Study, School of Social Science.
  17. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, vol. 60(5), pages 993-1008, September.
  18. Serrano, Roberto & Vohra, Rajiv, 2001. "Some Limitations of Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 69(3), pages 785-92, May.
  19. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July.
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Cited by:

  1. Geoffroy de Clippel & Rene Saran & Roberto Serrano, 2014. "Mechanism Design with Bounded Depth of Reasoning and Small Modeling Mistakes," Working Papers 2014-7, Brown University, Department of Economics.
  2. Chen, Yi-Chun & Kunimoto, Takashi & Sun, Yifei, 2015. "Implementation with Transfers," Discussion Papers 2015-04, Graduate School of Economics, Hitotsubashi University.
  3. Oury, Marion, 2015. "Continuous implementation with local payoff uncertainty," Journal of Economic Theory, Elsevier, vol. 159(PA), pages 656-677.
  4. Pivato, Marcus, 2013. "Statistical utilitarianism," MPRA Paper 49561, University Library of Munich, Germany.
  5. Müller, Christoph, 2016. "Robust virtual implementation under common strong belief in rationality," Journal of Economic Theory, Elsevier, vol. 162(C), pages 407-450.
  6. Marcus Pivato, 2014. "Asymptotic utilitarianism in scoring rules," THEMA Working Papers 2014-16, THEMA (THéorie Economique, Modélisation et Applications), Université de Cergy-Pontoise.

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