We show how norms can solve the distributional conflict inside a group in an anarchic environment and yield efficient coordination of collective action in a conflict with an external competitor. The equilibrium of the fully non-cooperative game with finite horizon has two interesting features. First, one of the players assumes a central role that resembles the role of the 'big-man' in some primitive stateless societies. Second, the group members' contributions to collective output and the payments from the big-man to these members seemingly look like reciprocal behavior, even though they are driven by narrowly selfish preferences.