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This paper examines repeated implementation of a Social Choice Function (SCF) with infinitely-lived agents whose preferences are determined randomly in each period. An SCF is repeated-implementable in (Bayesian) Nash equilibrium if there exists a sequence of (possibly history-dependent) mechanisms such that its equilibrium set is non-empty and every equilibrium outcome corresponds to the desired social choice at every possible history of past play and realizations of uncertainty. The authors first show, with minor qualifications, that in the complete information environment an SCF is repeated-implementable if and only if it is efficient. They then extend this result to the incomplete information setup.
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