Approximate efficiency in repeated games with side-payments and correlated signals

Side-payments are common in many long-term relationships. We show that when players can exchange side-payments, approximate efficiency is achievable in any repeated game with private monitoring and communication, as long as the players can observe their own payoffs and are sufficiently patient, the efficient stage-game outcome is unique, and the signal distribution has full support. Unlike existing results in the literature, our result does not require deviations to be statistically detectable.