Check Your Partners' Behavior by Randomization: New Efficiency Results on Repeated Games with Imperfect Monitoring

Randomization is an effective way of extracting information from a limited number of observations, as random auditing shows. We employ this idea to support efficient outcomes in repeated games with imperfect monitoring, when information is severely limited. In particular, we show that efficiency can be improved when the players randomize and condition their future actions both on the signal and their actions. Firstly, we show that in a version of Radner, Myerson and Maskin's example of inefficient partnership, efficiency can be achieved by such (i.e., privately mixed strategy) equilibria. Secondly, we show that the folk theorem under imperfect public monitoring can be extended to the case with a small signal space by means of mixed strategy equilibria with communication. In particular, we show that for generic symmetric games with at least four players, we can drop the Fudenberg-Levine-Maskin condition on the number of actions and signals altogether and prove the folk theorem under the same condition as in the perfect monitoring case.