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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- Postlewaite, Andrew & Schmeidler, David, 1986. "Implementation in differential information economies," Journal of Economic Theory, Elsevier, vol. 39(1), pages 14-33, June.
- 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.
- Palfrey, Thomas R & Srivastava, Sanjay, 1987. "On Bayesian Implementable Allocations," Review of Economic Studies, Wiley Blackwell, vol. 54(2), pages 193-208, April.
- Palfrey, Thomas R & Srivastava, Sanjay, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-34, January.
- Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March.
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