Decisions to engage in collaborative interactions require enduring considerable risk, yet provide the foundation for building and maintaining relationships. Here, we investigate the mechanisms underlying this process and test a computational model of social value to predict collaborative decision making. Twenty-six participants played an iterated trust game and chose to invest more frequently with their friends compared with a confederate or computer despite equal reinforcement rates. This behavior was predicted by our model, which posits that people receive a social value reward signal from reciprocation of collaborative decisions conditional on the closeness of the relationship. This social value signal was associated with increased activity in the ventral striatum and medial prefrontal cortex, which significantly predicted the reward parameters from the social value model. Therefore, we demonstrate that the computation of social value drives collaborative behavior in repeated interactions and provide a mechanistic account of reward circuit function instantiating this process.