This study uses fMRI to investigate the cognitive demands of decision-making in two types of cooperation games: a prisoner's dilemma (PD) eliciting a temptation to free-ride, leading to a dominant, self-interested response, and a stag hunt (SH) that has no dominant response but offers pay-off incentives that make mutual cooperation collectively beneficial but risky. Consequently, the PD poses greater conflict between self-and collective interest, greater demands for computational reasoning to derive the optimal solution, and greater demands for mentalizing to infer the intentions of others. Consistent with these differences between the two games, the results indicate that the PD is associated with increased activity in the anterior cingulate gyrus, prefrontal cortex, parietal lobe, and temporoparietal junction. With less conflict, the demands for computation and mentalizing are reduced in the SH, and cooperation levels increase dramatically. The differences in brain activation elicited by the different incentive structures of the PD and the SH appear to be independent of individual differences in revealed social preferences.