Using a multiround version of an economic exchange (trust game), we report that reciprocity expressed by one player strongly predicts future trust expressed by their partner-a behavioral finding mirrored by neural responses in the dorsal striatum. Here, analyses within and between brains revealed two signals-one encoded by response magnitude, and the other by response timing. Response magnitude correlated with the "intention to trust" on the next play of the game, and the peak of these "intention to trust" responses shifted its time of occurrence by 14 seconds as player reputations developed. This temporal transfer resembles a similar shift of reward prediction errors common to reinforcement learning models, but in the context of a social exchange. These data extend previous model-based functional magnetic resonance imaging studies into the social domain and broaden our view of the spectrum of functions implemented by the dorsal striatum.