We examine the possibility of cooperation in a long term relationship, where agents receive diverse imperfect information about each other's actions. "Secret price cutting" in the industrial organization literature is a leading example. In a differentiated product market, a firm cannot directly observe rival firms' secret price cutting, but its own sales can imperfectly indicate what is going on. Since the firms' sales levels are subject to random shocks, they may well end up having diverse expectations: firms with low sales may suspect price cutting while others may not. This causes a serious difficulty in sustaining collusion in such a market. In fact, the characterization of equilibria of this class of games-discounted repeated games where each player receives a different signal-has been an open question, despite the large body of literature on repeated games. The present paper shows that communication is a powerful way of resolving the possible confusion among the players in this class of games. In particular, we construct equilibria where players voluntarily communicate what they have observed and prove folk theorems. Our results thus provide a theoretical support for the conventional wisdom that communication plays an important role in sustaining collusion.