Social interactions routinely lead to neural activity in a "social brain network" comprising, among other regions, the temporoparietal junction (TPJ) and the dorsomedial prefrontal cortex (dmPFC). But what is the function of these areas? Are they specialized for behavior in social contexts or do they implement computations required for dealing with any reactive process, even non-living entities? Here, we use fMRI and a game paradigm separating the need for these two aspects of cognition. We find that most social-brain areas respond to both social and non-social reactivity rather than just to human opponents. However, the TPJ shows a dissociation from the dmPFC: its activity and connectivity primarily reflect context-dependent outcome processing and reactivity detection, while dmPFC engagement is linked to implementation of a behavioral strategy. Our results characterize an overarching computational property of the social brain but also suggest specialized roles for subregions of this network.