Problems of cooperation are frequent among living organisms, but they are difficult to solve. Humans have been able to produce large-scale cooperation among unrelated individuals through reputation systems. A challenging puzzle, however, is how reputation can guide behavior if in most cases it is not shared publicly and is assigned to others privately. We confirm that it is difficult to obtain cooperation among agents playing the Prisoners Dilemma when reputations are individually assigned. We propose that third-party communication (gossip) can overcome this difficulty, but only under specific conditions concerning its content, amount and persistence. We show that-in order to sustain cooperation-gossip should not only be about private evaluations of others but should also include perspective taking and exchange of information about tolerance thresholds to support cooperation. This perspective taking reputational strategy can propagate and establish cooperation in the population independent of gossip frequency and population size, under various selection mechanisms of communication partners and targets, and assumptions concerning agents memory.