Compliance-Based Theory economics, the article focuses explicitly on international law, explaining why countries care about it, and why they will expend resources in order to avoid violating it(or being perceived to violate it) The Article offers a reply to critics who argue that international law does not matter. To the extent those arguments are based on a theoretical claim, this Article demonstrates that it is possible to construct a theory of rational self-interested states in which international law does, in fact matter. Because the model is consistent with both conventional wisdom and empirical evidence showing that international law matters, as ll as the observation that the law is sometimes violated, it offers support to the longstanding claims of international legal scholars that international law affects the behavior of states On the other hand, the model also raises fundamental questions about international law as it is currently studied. By taking the question of compliance seriously, we gain a new perspective on international law, and that new perspective forces us to question some of the central issues in international law First, the analysis suggests the need for a new definition of customary international law(CIL). The existing definition of Cil has been the subject of a great deal of criticism, and some have gone so far as to suggest that no such law exists. 9 Rather than attempting to salvage the traditional definition, this article proposes a new one that focuses on whether or not a rule of customary international law affects behavior. It is shown that the requirements of widespread state practice and a sense of legal obligation do not contribute to a useful understanding of CIL. By studying CiL within a reputational model, and with a focus on compliance, it is possible to achieve a deeper understanding of that form of international law. Second, the Article proposes a new, functional definition of international law Once international law is considered from the perspective of compliance, it is clear that the classical definition of international lay w Is under- inclusive, and should be broadened to include not only treaties and customary international law, but also agreements such as ministerial accords, memoranda of understanding, and so on. Like treaties and customary international law, these instruments affect the incentives of countries and, therefore, should be considered international law Including them allows us to study the full range of international obligations within a single theoretical framework, and, unlike traditional theories, explains why such agreements exist and why Third, it is demonstrated that international law is most likely to affect outcome when there are many repeated interactions and each of those interactions involves See, e.g., Beth A. Simmons and the Law: Why Comply with the Public International Law of Money, 25 YALE J NT'L L 323(presenting empirical evidence that intermational law impacts government behavior See infra v BCompliance-Based Theory 3 economics, the article focuses explicitly on international law, explaining why countries care about it, and why they will expend resources in order to avoid violating it (or being perceived to violate it). The Article offers a reply to critics who argue that international law does not matter. To the extent those arguments are based on a theoretical claim, this Article demonstrates that it is possible to construct a theory of rational self-interested states in which international law does, in fact, matter. Because the model is consistent with both conventional wisdom and empirical evidence showing that international law matters,8 as well as the observation that the law is sometimes violated, it offers support to the longstanding claims of international legal scholars that international law affects the behavior of states. On the other hand, the model also raises fundamental questions about international law as it is currently studied. By taking the question of compliance seriously, we gain a new perspective on international law, and that new perspective forces us to question some of the central issues in international law. First, the analysis suggests the need for a new definition of customary international law (CIL). The existing definition of CIL has been the subject of a great deal of criticism, and some have gone so far as to suggest that no such law exists.9 Rather than attempting to salvage the traditional definition, this Article proposes a new one that focuses on whether or not a rule of customary international law affects behavior. It is shown that the requirements of widespread state practice and a sense of legal obligation do not contribute to a useful understanding of CIL. By studying CIL within a reputational model, and with a focus on compliance, it is possible to achieve a deeper understanding of that form of international law. Second, the Article proposes a new, functional definition of international law. Once international law is considered from the perspective of compliance, it is clear that the classical definition of “international law” is under-inclusive, and should be broadened to include not only treaties and customary international law, but also agreements such as ministerial accords, memoranda of understanding, and so on. Like treaties and customary international law, these instruments affect the incentives of countries and, therefore, should be considered international law. Including them allows us to study the full range of international obligations within a single theoretical framework, and, unlike traditional theories, explains why such agreements exist and why they are so popular. Third, it is demonstrated that international law is most likely to affect outcomes when there are many repeated interactions and each of those interactions involves 8 See, e.g., Beth A. Simmons, Money and the Law: Why Comply with the Public International Law of Money, 25 YALE J. INT’L L. 323 (presenting empirical evidence that international law impacts government behavior). 9 See infra V.B