A Note on Jackson's Theorems in Bayesian Implementation

Saglam, Ismail (1997): A Note on Jackson's Theorems in Bayesian Implementation.

Abstract

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.

• Item Type: MPRA Paper
• Language: English
• Keywords: Bayesian implementation; incomplete information
• Subjects: D - Microeconomics > D7 - Analysis of Collective Decision-Making > D70 - General; D - Microeconomics > D7 - Analysis of Collective Decision-Making > D71 - Social Choice ; Clubs ; Committees ; Associations

References

Jackson, M.O. (1991): "Bayesian Implementation," Econometrica, 59, 461-477

Palfrey, T., and S. Srivastava (1987): "On Bayesian Implementable Allocations," Review of Economic Studies, 54, 193-208

Palfrey, T., and S. Srivastava (1989a): "Mechanism Design with Incomplete Information: A Solution to the Implementation Problem," Journal of Political Economy, 97, 668-691

Palfrey, T., and S. Srivastava (1989b): "Implementation with Incomplete Information in Exchange Economies," Econometrica, 57, 115-134

Postlewaite, A., and D. Schmeidler (1986): "Implementation in Differential Information Economies," Journal of Economic Theory, 39, 14-33