Though competition and cooperation are often considered opposing forces in an arms race driving natural selection, many animals, including humans, cooperate in order to mitigate competition with others. Understanding others’ psychological states, such as seeing and knowing, others’ goals and intentions, and coordinating actions are all important for complex cooperation—as well as for predicting behavior in order to take advantage of others through tactical deception, a form of competition. We outline evidence of primates’ understanding of how others perceive the world, and then consider how the evidence from both deception and cooperation fits this framework to give us a more complete understanding of the evolution of complex social cognition in primates. In experimental food competitions, primates flexibly manipulate group-mates’ behavior to tactically deceive them. Deception can infiltrate cooperative interactions, such as when one takes an unfair share of meat after a coordinated hunt. In order to counter competition of this sort, primates maintain cooperation through partner choice, partner control, and third party punishment. Yet humans appear to stand alone in their ability to understand others’ beliefs, which allows us not only to deceive others with the explicit intent to create a false belief, but it also allows us to put ourselves in others’ shoes to determine when cheaters need to be punished, even if we are not directly disadvantaged by the cheater.