A Note on Jackson's Theorems in Bayesian Implementation
This note shows that in an incomplete information situation the closure condition will be satisfied by all social choice sets if and only if the set of states of the society which all agents believeoccur with positive probability satisfies the `connection' condition.It then follows from Jackson''s  fundamental theorems that whenever `connection'' is satisfied and there are at least three agents in the society, for the implementability of social choice sets in Bayesian equilibrium the incentive compatibility and Bayesian monotonicity conditions are both necessary and sufficient in economic environments. It also follows that the incentive compatibility and monotonicity-no-veto conditions are sufficient in noneconomic environments.
Volume (Year): 3 (2008)
Issue (Month): 55 ()
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References listed on IDEAS
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- Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-134, January.
- Thomas R. Palfrey & Sanjay Srivastava, 1987.
"On Bayesian Implementable Allocations,"
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Oxford University Press, vol. 54(2), pages 193-208.
- Palfrey, Thomas R. & Srivastava, Sanjay., 1986. "On Bayesian Implementable Allocations," Working Papers 624, California Institute of Technology, Division of the Humanities and Social Sciences.
- 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 668-691, June.
- Palfrey, Thomas R. & Srivastava, Sanjay., 1987. "Mechanism Design with Incomplete Information: A Solution to the Implementation Problem," Working Papers 658, California Institute of Technology, Division of the Humanities and Social Sciences.
- Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-477, March.
- Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June. Full references (including those not matched with items on IDEAS)