During social interactions, each individual's actions are simultaneously a consequence of and an antecedent to their interaction partner's behavior. Capturing online the brain processes underlying such mutual dependency requires simultaneous measurements of all interactants' brains during real-world exchange (hyperscanning'). This demands a precise characterization of the type of interaction under investigation, however, and analytical techniques capable of capturing interpersonal dependencies. We adapted an interactive task capable of dissociating between two dimensions of interdependent social exchange: goal structure (cooperation vs competition) and interaction structure [concurrent (CN) vs turn-based]. Performing dual-functional magnetic resonance imaging hyperscanning on pairs of individuals interacting on this task, and modeling brain responses in both interactants as systematic reactions to their partner's behavior, we investigated interpersonal brain-behavior dependencies (iBBDs) during each dimension. This revealed patterns of iBBDs that differentiated among exchanges; in players supporting the actions of another, greater brain responses to the co-player's actions were expressed in regions implicated in social cognition, such as the medial prefrontal cortex, precuneus and temporal cortices. Stronger iBBD during CN competitive exchanges was observed in brain systems involved in movement planning and updating, however, such as the supplementary motor area. This demonstrates the potential for hyperscanning to elucidate neural processes underlying different forms of social exchange.