Choosing how to cooperate: A repeated publicgoods model of international relations

International relations theory has borrowed important intuitions from Olson’s static public-goods model (hegemonic stability) and the repeated prisoners ’ dilemma (theories of international cooperation), and arguments often combine implications from both models. We develop a general, repeated public-goods model. We then allow the qualitative dimensions of cooperation to emerge endogenously: agree-ments can have broad or narrow membership and entail deep or shallow commitments; they can be multilateral or discriminatory; they can be ad hoc or institutionalized. We find that the relationship between the distri-bution of power and international cooperation is complex: a large lead-ing state forms a narrow coalition of intensive contributors, and builds institutions, while a smaller leading state forms a broader coalition that makes shallow contributions, and is more inclined to multilateralism. Theories of international cooperation generally make use of two key concepts drawn from formal theory: (1) the underprovision of public goods, and (2) the reputational benefits of repetition in cooperation games. However, most models that are used to derive these intuitions only incorporate one of these two fea-tures, and there is no reason to expect the intuitions to survive in a more gen-eral model. Most theories of international public goods are based implicitly or explicitly on a static models (Gowa 1989; Olson and Zeckhauser 1966; Oye 1992; Snidal 1985). On the other hand, theories that are based on repeated-game models, such as the repeated prisoners ’ dilemma, do not explicitly model cooperation as provision of a public good (Axelrod 1984; Keohane 1984; Krasner Authors ’ note: Randall W. Stone is the corresponding author (randall.stone@rochester.edu). We thank Robert Keohane, Andy Kydd, Robert Pahre, and Duncal Snidal for useful comments on an earlier version. The replication package can be found a