The Role of Reciprocity in International Law

International public law, in a Hobbesian sense, exists in a state of nature - there is no overarching legal authority to enforce agreements. Inevitably, reciprocity has become an important element in the body of existing law. This paper explores the role of reciprocity in the context of the law of nations. This paper draws on earlier work to characterize certain types of interactions between countries in a game-theoretic framework. We then consider the types of games where reciprocity constraints would yield an optimal outcome, and when such constraints would be ineffective, in the context of examples from international law. No external reciprocity constraint is necessary to achieve the Pareto optimum when the interests of all players coincide, as in a Common Interest game. In such a case, the reciprocity condition is termed structural. We find that different types of external reciprocity constraints are effective in Prisoner's Dilemma and Divergent Preference (Battle of the Sexes) games. Induced reciprocity, which eliminates the off-diagonal options is sufficient to get the players out of Prisoner's Dilemma. Stochastic reciprocity, based on the concept of role reversibility, can result in cooperation in a repeat Divergent Preference game. Reciprocity constraints are not effective in achieving cooperation in fixed sum games, or in what we term Unilateral games, where one player has a dominant strategy, regardless of what the other player does, and each player's dominant strategy could differ. We examine a number of areas of international law, including the law on the Continental Shelf, the GATT regime, the Law of the Sea and the CTBT to analyze the role of reciprocity. In view of the prevalence of reciprocity in the major sources of international law - treaties, custom and generalized principles - we conclude that, despite the occasional failure, as in the case of the CTBT, reciprocity is a meta-rule in international law.