In this paper we show how the possibility of recording simultaneously the cerebral neuroelectric activity in different subjects (EEG hyperscanning) during the execution of different tasks can return useful information about the "internal" cerebral state of the subjects. We present the results obtained by EEG hyperscannings during ecological task (such as the execution of a card game) as well as those obtained in couples of subjects during the performance of the Prisoner's Dilemma Game. The simultaneous recordings of couples of interacting subjects allows to observe and to model directly the neural signature of human interactions in order to understand the cerebral processes generating and generated by social cooperation or competition. Results obtained in a study of different groups recorded during the card game revealed a larger activity in prefrontal and anterior cingulated cortex in different frequency bands for the player that leads the game when compared to other players. Results collected in a population of 10 subjects during the performance of the Prisoner's Dilemma suggested that the most consistently activated structure is the orbitofrontal region (roughly described by the Brodmann area 10) during the condition of competition in both the tasks. It could be speculated whether the pattern of cortical connectivity between different cortical areas in different subjects could be employed as a tool for assessing the outcome of the task in advance.