Competition is ubiquitous among social animals. Vying against a conspecific to achieve a particular outcome often requires one to act aggressively, but this is a costly and inherently risky behavior. So why do we aggressively compete, or at the extreme, fight against others? Early work suggested that competitive aggression might stem from an innate aggressive tendency, emanating from subcortical structures. Later work highlighted key cortical regions that contribute toward an instrumental aggression network, one that is recruited or suppressed as needed to achieve a goal. Recent neuroimaging work hints that competitive aggression is upmost a cost-benefit decision, in that it appears to recruit many components of traditional, non-social decision-making networks. This review provides a historical glimpse into the neuroscience of competitive aggression, and proposes a conceptual advancement for studying competitive behavior by outlining how utility calculations of contested-for resources are skewed, pre- and post-competition. A basic multi-factorial model of utility assessment is proposed to account for competitive endowment effects that stem from the presence of peers, peer salience and disposition, and the tactical effort required for victory. In part, competitive aggression is a learned behavior that should only be repeated if positive outcomes are achieved. However, due to skewed utility assessments, deviations of associative learning occur. Hence truly careful cost-benefit analysis is warranted before choosing to vie against another.