Competitions are part and parcel of daily life and require people to invest time and energy to gain advantage over others and to avoid (the risk of) falling behind. Whereas the behavioral mechanisms underlying competition are well documented, its neurocognitive underpinnings remain poorly understood. We addressed this using neuroimaging and computational modeling of individual investment decisions aimed at exploiting one's counterpart (“attack”) or at protecting against exploitation by one's counterpart (“defense”). Analyses revealed that during attack relative to defense (i) individuals invest less and are less successful; (ii) computations of expected reward are strategically more sophisticated (reasoning level k = 4 vs. k = 3 during defense); (iii) ventral striatum activity tracks reward prediction errors; (iv) risk prediction errors were not correlated with neural activity in either ROI or whole-brain analyses; and (v) successful exploitation correlated with neural activity in the bilateral ventral striatum, left OFC, left anterior insula, left TPJ, and lateral occipital cortex. We conclude that, in economic contests, coming out ahead (vs. not falling behind) involves sophisticated strategic reasoning that engages both reward and value computation areas and areas associated with theory of mind.