Several theories have been generated to understand the socio-cognitive mechanisms underlying the unique cooperative abilities of humans. The ‘interdependence hypothesis' posits first, that the cognitive dimension of human cooperation evolved in contexts when several individuals needed to act together to achieve a common goal, like when hunting large prey. Second, the more interdependent individuals are, the more likely they are to provide services to conspecifics in other contexts. Alternatively, the ‘social tolerance hypothesis' proposes that higher social tolerance allows conspecifics to cooperate more efficiently and with a wider range of partners. We conducted the first field experimental evaluation of both hypotheses in our closest living relatives by contrasting chimpanzees to the less interdependent but more tolerant bonobos. We compared each species' performance during a cooperative task: informing conspecifics about a danger. We presented Gaboon viper models to 82 individuals from five wild communities. Chimpanzees arriving late at the snake were significantly more likely to have heard a call and less likely to startle, indicating that chimpanzees were better informed about the presence of the threat than bonobos. This stems from clear species differences in how individuals adjusted their calling decisions to the level of information already available. Chimpanzees were more likely to call and produced more alarm calls when they had not yet heard a call, whereas bonobos did so when they already heard a call. Our results confirm the link between interdependence and cooperation performance. These species differences were most likely driven by differences in motivation rather than in cognitive capacities because both species tended to consider audience knowledge in their decision to call. Our results inform theories on the evolution of human cooperation by linking inter-group competition pressure and in-group cooperative motivation and/or capability.