Social interaction is a fundamental part of our daily lives; however, exactly how our brains use social cues to determine whether to cooperate without being exploited remains unclear. In this study, we used an electroencephalography (EEG) hyperscanning approach to investigate the effect of face-to-face contact on the brain mechanisms underlying the decision to cooperate or defect in an iterated version of the Prisoner's Dilemma Game. Participants played the game either in face-to-face or face-blocked conditions. The face-to-face interaction led players to cooperate more often, providing behavioral evidence for the use of these nonverbal cues in their social decision-making. In addition, the EEG hyperscanning identified temporal dynamics and inter-brain synchronization across the cortex, providing evidence for involvement of these regions in the processing of face-to-face cues to read each other's intent to cooperate. Most notably, the power of the alpha frequency band (8-13Hz) in the right temporoparietal region immediately after seeing a round outcome significantly differed between face-to-face and face-blocked conditions and predicted whether an individual would adopt a 'cooperation' or 'defection' strategy. Moreover, inter-brain synchronies within this time and frequency range reflected the use of these strategies. This study provides evidence for how the cortex uses nonverbal social cues to determine other's intentions, and highlights the significance of power in the alpha band and inter-brain phase synchronizations in high-level socio-cognitive processing.