Humans naturally synchronize their behavior with other people. However, although it happens almost automatically, adjusting behavior and conformity to others is a complex phenomenon whose neural mechanisms are still yet to be understood entirely. The present experiment aimed to study the oscillatory synchronization mechanisms underlying automatic dyadic convergence in an EEG hyperscanning experiment. Thirty-six people performed a cooperative decision-making task where dyads had to guess the correct position of a point on a line. A reinforcement learning algorithm was used to model different aspects of the participants’ behavior and their expectations of their peers. Intra- and inter-connectivity among electrode sites were assessed using inter-site phase clustering in three main frequency bands (theta, alpha, beta) using a two-level Bayesian mixed-effects modeling approach. The results showed two oscillatory synchronization dynamics related to attention and executive functions in alpha and reinforcement learning in theta. In addition, inter-brain synchrony was mainly driven by beta oscillations. This study contributes preliminary evidence on the phase-coherence mechanism underlying inter-personal behavioral adjustment.