We recorded neural activity in male monkeys playing a variant of the game 'chicken' in which they made decisions to cooperate or not cooperate to obtain rewards of different sizes. Neurons in the middle superior temporal sulcus (mSTS)-previously implicated in social perception-signaled strategic information, including payoffs, intentions of the other player, reward outcomes and predictions about the other player. Moreover, a subpopulation of mSTS neurons selectively signaled cooperatively obtained rewards. Neurons in the anterior cingulate gyrus, previously implicated in vicarious reinforcement and empathy, carried less information about strategic variables, especially cooperative reward. Strategic signals were not reducible to perceptual information about the other player or motor contingencies. These findings suggest that the capacity to compute models of other agents has deep roots in the strategic social behavior of primates and that the anterior cingulate gyrus and the mSTS support these computations.