Lies and Slander: The Implementation of Truth-telling in Repeated Matching Games with Private Monitoring

This paper studies the implementation of truth-telling in a repeated random matching prisoners’ dilemma where outcomes cannot be observed or verified by the public. It is well established that truthful information sharing can be a powerful device to overcome moral hazard problems. An equilibrium strategy can ask players to condition their behavior on this shared information, which creates strong incentives for cooperation (public information strategy). The paper, first, shows that there is no direct mechanism which implements truth-telling in Nash equilibrium, subgame perfect equilibrium or any other equilibrium solution concept if an equilibrium outcome in the repeated game is supported by a public information strategy. Second, there is a mechanism which implements truth-telling in subgame perfect equilibrium if an equilibrium strategy in the repeated game asks players to condition their behavior on both, public and private information. However, if an outcome can be supported by this strategy, it can also be supported by a strategy without information sharing.