Human cooperation has been explained through rationality as well as heuristics-based models. Both model classes share the feature that knowledge of payoff functions is weakly beneficial for the emergence of cooperation. Here, we present experimental evidence to the contrary. We let human subjects interact in a competitive environment and find that, in the long run, access to information about own payoffs leads to less cooperative behaviour. In the short run subjects use naive learning heuristics that get replaced by better adapted heuristics in the long run. With more payoff information subjects are less likely to switch to pro-cooperative heuristics. The results call for the development of two-tier models for the evolution of cooperation.