The Customary International Law Supergame February 23, 2004 This conclusion is inescapable in theory, given the constraints of the game: by definition, the outcome of the prisoners dilemma game is an inefficient strategic equilibrium. This conclusion presents a normative goal: to modify the real world circumstances so as to produce stable equilibria that are efficient. This is the major role of CIL, and of international law generally respo. Of course, in a world of effective third-party enforcement of agreements,the response to the prisoner's dilemma is clear: the parties enter into a binding agreement to cooperate, thereby modifying the payoff structure and escaping the prisoner's dilemma The prisoners dilemma assumes, however, that its prisoners are held separately and have violated the law, so they cannot negotiate, reach or enforce a binding agreement. In the CIl setting, there is no court of general mandatory jurisdiction nor any publicly-appointed"policeman. While we may draw analogies to the World Court and the U.N., these institutions have substantial differences compared to domestic courts and police. Therefore, we begin by assuming that there is no capacity to make agreements that are binding. This is obviously a simplifying assumption. Our model is meant to show that there are substitutes for formal binding agreements In the cil game, there are five important distinctions from the assumptions of the players can communicate with one another, and can do so more readily today th 5 non-cooperative game theory in general, and the prisoner's dilemma in particular. Fi during the classical period of formation of CIL. Second, the players can enter into treaties that are at least somewhat binding. Third, states play an iterated game with one another with no defined end date, and so can respond at a later time to something done at an earlier time. Updating of information and punishment are possible. Fourth, not only is the narrow game characterized by a particular Cil rule, like the three-mile territorial sea, but it is embedded in a dense fabric of relationships. Fifth, information regarding compliance is often readily accessible; more so today, it would appear, than during the 19century. Each of these distinctions alone may be sufficient to transform the game into something quite different from the prisoners dilemma-while nothing resolves the true prisoner's dilemma, modifications may result in stable and efficient equilibria Indeed, it may be useful to use cooperative game theory to analyze some Cil circumstances As will be illustrated below, one of the more difficult types of multilateral cooperation problem is a commons problem in which, as in the cartel context, incentives to defect increase with the number of other states that comply. where incentives to defect increase with the number of players, we would expect the most severe challenge to cooperation. Not all Cil contexts exhibit this characteristic For an application of cooperative game theory in the international context, see Daniel G. Arce M. Todd Sandler, A Cooperative Game Theory of Non-Contiguous Allies, 3 J PUB. ECoN THEORY 391(2000)(applying cooperative game theory to international security arrangementsThe Customary International Law Supergame February 23, 2004 12 This conclusion is inescapable in theory, given the constraints of the game: by definition, the outcome of the prisoner’s dilemma game is an inefficient strategic equilibrium. This conclusion presents a normative goal: to modify the real world circumstances so as to produce stable equilibria that are efficient. This is the major role of CIL, and of international law generally. Of course, in a world of effective third-party enforcement of agreements, the response to the prisoner’s dilemma is clear: the parties enter into a binding agreement to cooperate, thereby modifying the payoff structure and escaping the prisoner’s dilemma. The prisoner’s dilemma assumes, however, that its prisoners are held separately and have violated the law, so they cannot negotiate, reach or enforce a binding agreement. In the CIL setting, there is no court of general mandatory jurisdiction nor any publicly-appointed “policeman.” While we may draw analogies to the World Court and the U.N., these institutions have substantial differences compared to domestic courts and police. Therefore, we begin by assuming that there is no capacity to make agreements that are binding. This is obviously a simplifying assumption. Our model is meant to show that there are substitutes for formal binding agreements. In the CIL game, there are five important distinctions from the assumptions of non-cooperative game theory in general, and the prisoner’s dilemma in particular. First, the players can communicate with one another, and can do so more readily today than during the classical period of formation of CIL. Second, the players can enter into treaties that are at least somewhat binding. Third, states play an iterated game with one another with no defined end date, and so can respond at a later time to something done at an earlier time. Updating of information and punishment are possible. Fourth, not only is the narrow game characterized by a particular CIL rule, like the three-mile territorial sea, but it is embedded in a dense fabric of relationships. Fifth, information regarding compliance is often readily accessible; more so today, it would appear, than during the 19 th century. Each of these distinctions alone may be sufficient to transform the game into something quite different from the prisoner’s dilemma—while nothing resolves the true prisoner’s dilemma, modifications may result in stable and efficient equilibria. Indeed, it may be useful to use cooperative game theory to analyze some CIL circumstances. 38 As will be illustrated below, one of the more difficult types of multilateral cooperation problem is a commons problem in which, as in the cartel context, incentives to defect increase with the number of other states that comply. Where incentives to defect increase with the number of players, we would expect the most severe challenge to cooperation. Not all CIL contexts exhibit this characteristic. 38 For an application of cooperative game theory in the international context, see Daniel G. Arce M. & Todd Sandler, A Cooperative Game Theory of Non-Contiguous Allies, 3 J. PUB. ECON. THEORY 391 (2000) (applying cooperative game theory to international security arrangements)