Frequent Actions with Infrequent Coordination

I study repeated games with mediated communication and frequent actions. I derive a Folk Theorem with imperfect monitoring assuming a conditional form of individual identifiability. Even in the limit, when noise is driven by Brownian motion and actions are arbitrarily frequent, as long as players are sufficiently patient they can attain virtually efficient equilibrium outcomes, in two ways: secret monitoring and infrequent coordination. Players follow private strategies over discrete blocks of time. A mediator constructs latent Brownian motions to score players on the basis of others’ secret monitoring, and gives incentives with these variables at the end of each block, to improve information aggregation. This brings together the work on repeated games in discrete and continuous time in that, despite actions being continuous, strategic coordination is endogenously discrete. As an application, I show how (unconditional) individual identifiability is necessary and sufficient for the Folk Theorem in the Prisoners’ Dilemma. JEL Classification: D21, D23, D82.