Repeated Implementation with Incomplete Information

We formulate and analyze a model of (full) repeated implementation with incomplete information. A group of infinitely-lived agents possess state-dependent utilities over a set of outcomes and in each period a state is drawn independently from an identical prior distribution. Each agent privately observes some partial contents of a realized state and may condition behavior on his private information as well as publicly observable histories. It is shown that, with minor qualifications, a social choice function (SCF) that is efficient in the range and incentive compatible can be repeatedly implemented in Bayesian Nash equilibrium under the general information structure. When the agents' utilities are interdependent, incentive compatibility can be replaced with a payoff identifiability condition. We also show that efficiency in the range is sufficient for approximate repeated implementation in public strategies when the information structure satisfies certain statistical identifiability properties.

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