Abstract: This article presents a theory of customary international law ("CIL") that seeks to sort out the many well-known difficulties with standard accounts of CIL. The theory uses simple game theoretical concepts to explain how what we call CIL arises, why nations "comply" with CIL as commonly understood, and how CIL changes. This theory differs from the standard account of CIL in several fundamental respects. It rejects the usual explanations of CIL based on opinio juris, legality, morality, and related concepts. States do not comply with norms of CIL because of a sense of moral or legal obligation; rather, their compliance and the norms themselves emerge from the states' pursuit of self interested policies on the international stage. In addition, the behaviors associated with CIL do not reflect a single, unitary logic. Instead, they reflect various and importantly different logical structures played out in discrete, historically contingent contexts. Finally, the theory is skeptical of the existence of multilateral behavioral regularities that are typically thought to constitute CIL. The article tests the theory using case studies from four traditional areas of CIL: neutrality, diplomatic immunity, prize, and maritime jurisdiction. We find that most purported rules of CIL reflect pure coincidence of interest, rather than international cooperation, and that the rest are best explained as the outcome of repeated bilateral prisoner's dilemmas or coercion analogous to the behavior of the monopolist in predatory pricing games. We conclude by examining the implications of our analysis for understanding the role of CIL in domestic constitutional arrangements, the function of international treaties and international organizations, and the status of modern international human rights law.