Bayesian implementation in exchange economies with state dependent preferences and feasible sets

This paper considers Bayesian and Nash implementation in exchange economic environments with state dependent preferences and feasible sets. We fully characterize Bayesian implementability for both diffuse and non-diffuse information structures. We show that, in exchange economic environments with three or more individuals, a social choice set is Bayesian implementable if and only if closure, non-confiscatority, Bayesian monotonicity, and Bayesian incentive compatibility are satisfied. As such, it improves upon and contains as special cases previously known results about Nash and Bayesian implementation in exchange economic environments. We show that the individual rationality and continuity conditions, imposed in Hurwicz et al. [12], can be weakened to the non-confiscatority and can be dropped, respectively, for Nash implementation. Thus we also give a full characterization for Nash implementation when endowments and preferences are both unknown to the designer.