The implausibility of the extreme rationality assumptions of Nash equilibrium has been attested by numerous experimental studies with human players. In particular, the fundamental social dilemmas such as the Traveler?s dilemma, the Prisoner?s dilemma, and the Public Goods game demonstrate high rates of deviation from the unique Nash equilibrium, dependent on the game parameters or the environment in which the game is played. These results inspired several attempts to develop suitable solution concepts to more accurately explain human behaviour. In this line, the recently proposed notion of cooperative equilibrium, [5], [6], based on the idea that players have a natural attitude to cooperation, has shown promising results for single-shot games. In this paper, we extend this approach to iterated settings. Specifically, we define the Iterated Cooperative Equilibrium (ICE) and show it makes statistically precise predictions of population average behaviour in the aforementioned domains. Importantly, the definition of ICE does not involve any free parameters, and so it is fully predictive.