Peer-punishment is effective in promoting cooperation, but the costs associated with punishing defectors often exceed the benefits for the group. It has been argued that centralized punishment institutions can overcome the detrimental effects of peer-punishment. However, this argument presupposes the existence of a legitimate authority and leaves an unresolved gap in the transition from peer-punishment to centralized punishment. Here we show that the origins of centralized punishment could lie in individuals' distinct ability to punish defectors. In our laboratory experiment, we vary the structure of the punishment situation to disentangle the effects of punitive preferences, monetary incentives, and individual punishment costs on the punishment of defectors. We find that actors tacitly coordinate on the strongest group member to punish defectors, even if the strongest individual incurs a net loss from punishment. Such coordination leads to a more effective and more efficient provision of a cooperative environment than we observe in groups of all equals. Our results show that even an arbitrary assignment of an individual to a focal position in the social hierarchy can trigger the endogenous emergence of more centralized forms of punishment.