Social interactions routinely lead to neural activity in a so-called “social brain network” comprising, among other regions, the temporoparietal junction (TPJ) and the dorsomedial prefrontal cortex (dmPFC). But what is the behavioral function of these brain areas – are they specialized for interacting with others in social contexts or do they implement general-purpose computations required for dealing with any reactive process, even non-living entities? Here, we approach this question using functional magnetic resonance imaging (fMRI) and a novel game paradigm separating the need for these two (usually correlated) aspects of cognition. We find that most areas in the social-brain network respond to both social and non-social reactivity, rather than specifically to human opponents. However, the TPJ shows a functional dissociation from the dmPFC: Its activation and connectivity with reward-coding brain areas additionally differentiate between social and non-social contexts. Our results characterize an overarching computational property underlying the engagement of the social-brain network but also suggest specialized roles for different subregions of this network.