Little is known about brain mechanisms recruited during the monitoring and appraisal of social conflicts—for instance, when individuals compete with each other for the same resources. We designed a novel experimental task inducing resource conflicts between two individuals. In an event-related functional magnetic resonance imaging (fMRI) design, participants played with another human participant or against a computer, who across trials chose either different (no-conflict) or the same tokens (conflict trials) in order to obtain monetary gains. In conflict trials, the participants could decide whether they would share the token, and the resulting gain, with the other person or instead keep all points for themselves. Behaviorally, participants shared much more often when playing with a human partner than with a computer. fMRI results demonstrated that the dorsal mediofrontal cortex was selectively activated during human conflicts. This region might play a key role in detecting situations in which self- and social interest are incompatible and require behavioral adjustment. In addition, we found a conflict-related response in the right ventrolateral prefrontal cortex that correlated with measures of social relationship and individual sharing behavior. Taken together, these findings reveal a key role of these prefrontal areas for the appraisal and resolution of interpersonal resource conflicts.