The conditions under which humans benefit from contributing to a public good have attracted great interest; in particular the potential role of punishment of cheaters is hotly debated. In contrast, similar studies on other animals are lacking. In this study, we describe for the first time how the course of interactions between parasitic sabre-tooth blennies (the cheaters) and their reef fish victims can be used to study both punishment and the emergence of public goods. Sabre tooth blennies (Plagiotremus sp.) sneak up from behind to bite off small pieces of scales and/or mucus from other fish. Victims regularly show spontaneous aggression as well as aggressive responses to blenny attacks. In a between species comparison, we tested how the probability of chasing a blenny is affected by (1) the option of avoiding interactions with a blenny by avoiding its small territory, and (2) variation in local abundance of conspecifics. We found that resident victim species are more aggressive towards blennies than visiting species. This difference persisted when we controlled for victim size and territoriality, suggesting that it is the enforced repeated game structure that causes residents to chase blennies. In residents, we also found a negative correlation between aggression towards blennies and local abundance, which suggests that the benefits of chasing are diluted with increasing local abundance. We discuss the implication of these results for future studies.