The study of social dominance interactions between animals offers a window onto the decision-making involved in establishing dominance hierarchies and an opportunity to examine changes in social behavior observed in certain neurogenetic disorders. Competitive social interactions, such as in the widely used tube test, reflect this decision-making. Previous studies have focused on the different patterns of behavior seen in the dominant and submissive animal, neural correlates of effortful behavior believed to mediate the outcome of such encounters, and interbrain correlations of neural activity. Using a rigorous mutual information criterion, we now report that neural responses recorded with endoscopic calcium imaging in the prelimbic zone of the medial prefrontal cortex show unique correlations to specific dominance-related behaviors. Interanimal analyses revealed cell/behavior correlations that are primarily with an animal’s own behavior or with the other animal’s behavior, or the coincident behavior of both animals (such as pushing by one and resisting by the other). The comparison of unique and coincident cells helps to disentangle cell firing that reflects an animal’s own or the other’s specific behavior from situations reflecting conjoint action. These correlates point to a more cognitive rather than a solely behavioral dimension of social interactions that needs to be considered in the design of neurobiological studies of social behavior. These could prove useful in studies of disorders affecting social recognition and social engagement, and the treatment of disorders of social interaction.