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Abstract:
This paper unifes the theories of
Nash implementation and Bayesian implementation in
a single framework. Environments considered are such that
each agent's characteristics include,
in addition to a specifcation of his private information,
a commonly known type parameter, while both attributes are
unknown to the designer. Each social choice correspondence (SCC)
as-signs a commonly known
type vector to a social choice set, a collection of functions
mapping private type vectors to allocations Conditions
that fully characterize an implementable SCC in economic environments
where agents are not satiated generalize and merge respec-tive
conditions in the complete
information model of Danilov (1992) and the
incomplete information model of Jackson (1991). In noneconomic
envi-ronments there remains
to exist a gap between the necessary and su±cient conditions,
like in Jackson (1991). In order to narrow down this gap, we em-ploy
Danilov's notion of essential
elements and develop a stronger necessary condition,
termed essential-generalized-Bayesian monotonicity (EGBM).
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