A Unified Theory of Implementation

This paper unifies the theories of Nash implementation and Bayesian implementation. Environments considered are such that each agent's characteristics include, in addition to a specification of his private information, a commonly known type parameter, while both attributes are unknown to the designer. Each social choice correspondence (SCC) assigns a commonly known type vector to a social choice set. Conditions that fully characterize an implementable SCC in economic environments where agents are not satiated generalize and merge respective conditions in the complete information model of Danilov (1992) and the incomplete information model of Jackson (1991).