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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- Thomas R. Palfrey & Sanjay Srivastava, 1987.
"On Bayesian Implementable Allocations,"
Review of Economic Studies,
Oxford University Press, vol. 54(2), pages 193-208.
- Jackson, Matthew O, 1991. "Bayesian Implementation," Econometrica, Econometric Society, vol. 59(2), pages 461-77, March.
- 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.
"Mechanism Design with Incomplete Information: A Solution to the Implementation Problem,"
658, 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, 1989. "Implementation with Incomplete Information in Exchange Economies," Econometrica, Econometric Society, vol. 57(1), pages 115-34, January.
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