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International relations theory has borrowed important intuitions fromOlson'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: agreements 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 distribution of power and international cooperation is complex: a large leading 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 features, and there is no reason to expect the intuitions to survive in a more general 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; 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 at http://polisci.ucsd.edu/slantchev and the ISQ Dataverse at http://dvn.iq.harvard.edu/ dvn/dv/isq. It includes Aptech Gauss programs for the simulations and the complete proofs.