Integrating social robots in our group-based society, beyond the technical challenges, requires considering the social group dynamics. Following the results from preliminary exploratory studies on the influence of social robots on group decisions, the proposed research investigates whether social robots can foster cooperation among group members. To achieve this, I propose a game theory approach, employing the Public Good Game to recreate a simplified and controlled social situation where the robot's influence can be evaluated. Clarifying the role of robots in promoting collaboration among humans might have a significant impact in educational environments, enhancing student learning, as well as in workplace settings, where they could facilitate problem-solving and lead to shared solutions.