Brain mitochondrial function is critical for numerous neuronal processes. We recently identified a link between brain energy and social dominance, where higher levels of mitochondrial function resulted in increased social competitive ability. The underlying mechanism of this link, however, remains unclear. Here, we investigated the contribution of astrocytic release of adenosine triphosphate (ATP) through the type 2 inositol 1,4,5‐triphosphate receptor to social dominance behavior. Mice lacking the type 2 inositol 1,4,5‐triphosphate receptor were characterized for their social dominance behavior, as well as their performance on a nonsocial task, the Morris Water Maze. In parallel, we also examined mitochondrial function in the medial prefrontal cortex, nucleus accumbens, and hippocampus to investigate how deficiencies in astrocytic ATP could modulate overall mitochondrial function. While knockout mice showed similar competitive ability compared with their wild‐type littermates, dominant knockout mice exhibited a significant delay in exerting their dominance during the initial encounter. Otherwise, there were no differences in anxiety and exploratory traits, spatial learning and memory, or brain mitochondrial function in either light or dark circadian phases. Our findings point to a marginal role of astrocytic ATP through IP3R2 in social competition, suggesting that, under basal conditions, the neuronal compartment is predominant for social dominance exertion.