A Note on Jackson's Theorems in Bayesian Implementation
This paper shows that in an incomplete information situation if the set of states of the society which occur with positive probability satisfies 'connection' condition, then closure condition will be satisfied by all social choice sets. It then follows from Jackson's (1991) two fundamental theorems that whenever 'connection' holds and there are at least three agents in the society, for the implementability of social choice sets in Bayesian equilibrium, incentive compatibility and Bayesian monotonicity conditions are both necessary and sufficient in economic environments whereas incentive compatibility and monotonicity-no-veto conditions are sufficient in noneconomic environments.
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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, 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.
- 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.
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