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A Characterization of Virtual Bayesian Implementation

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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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Paper provided by Brown University, Department of Economics in its series Working Papers with number 2002-11.

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Date of creation: 2002
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Handle: RePEc:bro:econwp:2002-11

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Postal: Department of Economics, Brown University, Providence, RI 02912

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  1. Dutta Bhaskar & Sen Arunava, 1994. "Bayesian Implementation: The Necessity of Infinite Mechanisms," Journal of Economic Theory, Elsevier, Elsevier, vol. 64(1), pages 130-141, October.
  2. Abreu, Dilip & Matsushima, Hitoshi, 1992. "A Response [Virtual Implementation in Iteratively Undominated Strategies I: Complete Information]," Econometrica, Econometric Society, Econometric Society, vol. 60(6), pages 1439-42, November.
  3. Muller, Eitan & Satterthwaite, Mark A., 1977. "The equivalence of strong positive association and strategy-proofness," Journal of Economic Theory, Elsevier, Elsevier, vol. 14(2), pages 412-418, April.
  4. Serrano, Roberto & Vohra, Rajiv, 2001. "Some Limitations of Virtual Bayesian Implementation," Econometrica, Econometric Society, Econometric Society, vol. 69(3), pages 785-92, May.
  5. Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, Elsevier, vol. 39(1), pages 14-33, June.
  6. 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, University of Chicago Press, vol. 97(3), pages 668-91, June.
  7. Matsushima, Hitoshi, 1988. "A new approach to the implementation problem," Journal of Economic Theory, Elsevier, Elsevier, vol. 45(1), pages 128-144, June.
  8. Brusco, Sandro, 1995. "Perfect Bayesian Implementation," Economic Theory, Springer, Springer, vol. 5(3), pages 419-44, May.
  9. Moore, John & Repullo, Rafael, 1988. "Subgame Perfect Implementation," Econometrica, Econometric Society, Econometric Society, vol. 56(5), pages 1191-1220, September.
  10. Abreu, Dilip & Sen, Arunava, 1991. "Virtual Implementation in Nash Equilibrium," Econometrica, Econometric Society, Econometric Society, vol. 59(4), pages 997-1021, July.
  11. Bergin, James & Sen, Arunava, 1998. "Extensive Form Implementation in Incomplete Information Environments," Journal of Economic Theory, Elsevier, Elsevier, vol. 80(2), pages 222-256, June.
  12. 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, Department of Economics, University of Pennsylvania and Osaka University Institute of Social and Economic Research Association, vol. 33(1), pages 45-59, February.
  13. Matsushima Hitoshi, 1993. "Bayesian Monotonicity with Side Payments," Journal of Economic Theory, Elsevier, Elsevier, vol. 59(1), pages 107-121, February.
  14. Abreu, Dilip & Sen, Arunava, 1990. "Subgame perfect implementation: A necessary and almost sufficient condition," Journal of Economic Theory, Elsevier, Elsevier, vol. 50(2), pages 285-299, April.
  15. John Duggan, 1997. "Virtual Bayesian Implementation," Econometrica, Econometric Society, Econometric Society, vol. 65(5), pages 1175-1200, September.
  16. Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, Econometric Society, vol. 57(1), pages 115-34, January.
  17. Saijo, Tatsuyoshi, 1987. "On constant maskin monotonic social choice functions," Journal of Economic Theory, Elsevier, Elsevier, vol. 42(2), pages 382-386, August.
  18. Abreu, Dilip & Matsushima, Hitoshi, 1992. "Virtual Implementation in Iteratively Undominated Strategies: Complete Information," Econometrica, Econometric Society, Econometric Society, vol. 60(5), pages 993-1008, September.
  19. Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, Econometric Society, vol. 59(2), pages 461-77, March.
  20. Baliga, Sandeep, 1999. "Implementation in Economic Environments with Incomplete Information: The Use of Multi-Stage Games," Games and Economic Behavior, Elsevier, Elsevier, vol. 27(2), pages 173-183, May.
  21. Palfrey, Thomas R & Srivastava, Sanjay, 1987. "On Bayesian Implementable Allocations," Review of Economic Studies, Wiley Blackwell, Wiley Blackwell, vol. 54(2), pages 193-208, April.
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