Efficient Repeated Implementation∗

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 Nash equilibrium if there exists a sequence of (possibly history-dependent) mechanisms such that (i) its Nash equilibrium set is non-empty and (ii) every Nash equilibrium outcome corresponds to the desired social choice at every possible history of past play and realizations of uncertainty. We show, with minor qualifications, that in the complete information environment an SCF is repeated-implementable in Nash equilibrium if and only if it is efficient. We also discuss several extensions of our analysis, including constructions employing only finite mechanisms. JEL Classification: A13, C72, C73, D02, D70