Modern-day piracy on the high seas once again poses a serious threat to international shipping. This paper develops an economic of model of piracy that emphasizes the strategic interaction between pirates (offenders) and shippers (victims), a factor not previously studied in the law enforcement literature. A key implication of the model is that greater enforcement efforts will not necessarily result in less activity by pirates. Optimal enforcement policies are complicated by the need for international cooperation in the apprehension and prosecution of pirates. Free riding and other problems therefore impede the effectiveness of current international laws against piracy.