Social control and the enforcement of social norms glue a society together. It has been shown theoretically and empirically that informal punishment of wrongdoers fosters cooperation in human groups. Most of this research has focused on voluntary and uncoordinated punishment carried out by individual group members. However, as punishment is costly, it is an open question as to why humans engage in the punishment of wrongdoers even in one-time-only encounters. While evolved punitive preferences have been advocated as proximate explanations for such behaviour, the strategic nature of the punishment situation has remained underexplored. It has been suggested to conceive of the punishment situation as a volunteer's dilemma (VOD), where only one individual's action is necessary and sufficient to punish the wrongdoer. Here, we show experimentally that implementing the punishment situation as a VOD sustains cooperation in an environment where punishers and non-punishers coexist. Moreover, we show that punishment-cost heterogeneity allows individuals to tacitly agree on only the strongest group member carrying out the punishment, thereby increasing the effectiveness and efficiency of social norm enforcement. Our results corroborate that costly peer punishment can be explained without assuming punitive preferences and show that centralized sanctioning institutions can emerge from arbitrary individual differences.