The "intuitive" (fast) interaction heuristic is predisposed towards selflessness, while the "calculated" (slow) decision making process favors greedier behavior: review of game studies.
Sidenote: Strange to have a Nature paper conflate a faster-payoff / 'egoistic' approach with being 'rational', and to contrast intuition with calculation, of all things. As if not being consciously aware of the calculation implicit in fast "intuitive" decision algorithms implied a lack of cognitive processing.
I wonder if inducing a feeling of power/high status in people would change the cooperative nature of the immediate response. It seems like in a tribe, you cooperate unless you're sure you can get away with defecting.