So far, the theory of equilibrium selection in the infinitely repeated prisoner's dilemma is insensitive to communication possibilities. To address this issue, we incorporate the assumption that communication reduces -- but does not entirely eliminate -- an agent's uncertainty that the other agent follows a cooperative strategy into the theory. Because of this, agents still worry about the payoff from cooperating when the other one defects, i.e. the sucker's payoff S, and, games with communication are more conducive to cooperation than games without communication. This theory is supported by data from laboratory experiments, and by machine learning based evaluation of the communication content.