Social interactions in nonhuman primates involve complex communication, outcome evaluation, and behavioral adjustments. Social gaze is a vital mechanism for gathering information during such interactions. We investigated the role of social gaze in cooperative behavior among common marmosets (Callithrix jacchus) using a cooperative lever-pulling task in a naturalistic setting. Marmoset pairs were placed in separate transparent compartments with access to levers and juice tubes. Successful juice delivery required simultaneous lever-pulling, necessitating coordination. We recorded their behavior using a set of synchronized cameras and employed markerless tracking to analyze gaze directions and dynamics. We quantified social gaze instances and applied a Dynamic Bayesian Network (DBN) approach to explore the multivariate dynamics between gaze behavior and lever-pulling actions of the pair. Our analysis revealed systematic increases in causal dependencies between lever-pulling behaviors and between gaze and pull actions of the pair, indicating that marmosets integrate gaze-independent and gaze-dependent strategies to facilitate cooperation. Preliminary results from wireless recordings from the dorsolateral prefrontal cortex (dlPFC) demonstrated that neural populations in this region differentiate between the same actions driven by different strategies. This study underscores the significant role of social gaze in primate cooperative interactions and suggests a neural basis for strategy encodings in the dlPFC.