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A Characterization of Virtual Bayesian Implementation

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Author Info
Roberto Serrano () (Department of Economics, Brown University)
Rajiv Vohra () (Department of Economics, Brown University)

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Abstract

We provide a characterization of virtual Bayesian implementation in pure strategies for environments satisfying no-total-indifference. A social choice function in such environments is virtually Bayesian implementable if and only if it satisfies incentive compatibility and a condition we term virtual monotonicity. The latter is weaker than Bayesian monotonicity - known to be necessary for Bayesian implementation. Virtual monotonicity is weak in the sense that it is generically satisfied in environments with at least three alternatives. This implies that in most environments virtual Bayesian implementation is as successful as it can be (incentive compatibility is the only condition needed).

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Publisher Info
Paper provided by Institute for Advanced Study, School of Social Science in its series Economics Working Papers with number 0028.

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Length: 27 pages
Date of creation: Nov 2002
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Handle: RePEc:ads:wpaper:0028

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Related research
Keywords: Virtual monotonicity; Bayesian monotonicity; Maskin monotonicity; virtual Bayesian implementation; incentive compatibility; type diversity; decentralization; incomplete information;

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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-Making and Implementation
D82 - Microeconomics - - Information, Knowledge, and Uncertainty - - - Asymmetric and Private Information

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:

  1. Muller, Eitan & Satterthwaite, Mark A., 1977. "The equivalence of strong positive association and strategy-proofness," Journal of Economic Theory, Elsevier, vol. 14(2), pages 412-418, April. [Downloadable!] (restricted)
  2. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-34, January. [Downloadable!] (restricted)
  3. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, vol. 45(1), pages 128-144, June. [Downloadable!] (restricted)
  4. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June. [Downloadable!] (restricted)
  5. Brusco, Sandro, 1995. "Perfect Bayesian Implementation," Economic Theory, Springer, vol. 5(3), pages 419-44, May.
  6. 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. [Downloadable!] (restricted)
  7. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Mechanism Design with Incomplete Information: A Solution to the Implementation Problem," Journal of Political Economy, University of Chicago Press, vol. 97(3), pages 668-91, June. [Downloadable!] (restricted)
  8. Serrano, Roberto & Vohra, Rajiv, 2001. "Some Limitations of Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 69(3), pages 785-92, May.
  9. Dutta Bhaskar & Sen Arunava, 1994. "Bayesian Implementation: The Necessity of Infinite Mechanisms," Journal of Economic Theory, Elsevier, vol. 64(1), pages 130-141, October. [Downloadable!] (restricted)
  10. Saijo, Tatsuyoshi, 1987. "On constant maskin monotonic social choice functions," Journal of Economic Theory, Elsevier, vol. 42(2), pages 382-386, August. [Downloadable!] (restricted)
  11. Matsushima Hitoshi, 1993. "Bayesian Monotonicity with Side Payments," Journal of Economic Theory, Elsevier, vol. 59(1), pages 107-121, February. [Downloadable!] (restricted)
  12. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, vol. 65(5), pages 1175-1200, September.
  13. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March. [Downloadable!] (restricted)
  14. Bergin, James & Sen, Arunava, 1998. "Extensive Form Implementation in Incomplete Information Environments," Journal of Economic Theory, Elsevier, vol. 80(2), pages 222-256, June. [Downloadable!] (restricted)
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  15. Palfrey, Thomas R & Srivastava, Sanjay, 1987. "On Bayesian Implementable Allocations," Review of Economic Studies, Blackwell Publishing, vol. 54(2), pages 193-208, April. [Downloadable!] (restricted)
  16. Abreu, D. & Matsushima, H., 1991. "Virtual Implementation in Iteratively Undominated Strategies: Incomplete Information," Papers e-91-2, Stanford - Hoover Institution.
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  17. Baliga, Sandeep, 1999. "Implementation in Economic Environments with Incomplete Information: The Use of Multi-Stage Games," Games and Economic Behavior, Elsevier, vol. 27(2), pages 173-183, May. [Downloadable!] (restricted)
  18. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, vol. 59(4), pages 997-1021, July. [Downloadable!] (restricted)
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Full references

Cited by:
(explanations, Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.)

  1. Dino Gerardi & Richard McLean & Andrew Postlewaite, 2005. "Aggregation of Expert Opinions," PIER Working Paper Archive 05-016, Penn Institute for Economic Research, Department of Economics, University of Pennsylvania. [Downloadable!]
    Other versions:
  2. Georgy Artemov & Takashi Kunimoto & Roberto Serrano, 2007. "Robust Virtual Implementation with Incomplete Information: Toward a Reinterpretation of the Wilson Doctrine," Working Papers 2007-6, Brown University, Department of Economics. [Downloadable!]
    Other versions:
  3. Dirk Bergemann & Stephen Morris, 2005. "Robust Implementation: The Role of Large Type Spaces," Levine's Bibliography 784828000000000116, UCLA Department of Economics. [Downloadable!]
    Other versions:
  4. Antonio Cabrales & Roberto Serrano, 2007. "Implementation in adaptive better-response dynamics," Working Papers 2007-16, Instituto Madrileño de Estudios Avanzados (IMDEA) Ciencias Sociales. [Downloadable!]
    Other versions:
  5. Hitoshi Matsushima, 2004. "On Detail-Free Mechanism Design and Rationality," CIRJE F-Series CIRJE-F-287, CIRJE, Faculty of Economics, University of Tokyo. [Downloadable!]
    Other versions:
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