The study of political institutions in general and international cooperation in particular has been beneficially influenced by the Prisoners' Dilemma (PD) game model, but there is a mistaken tendency to treat PD as representing the singular problem of collective action and cooperation. By relaxing the assumptions of 2 × 2 games and developing an alternate model of the coordination game, I show how some cooperation problems have very different properties from those found in PD. The analytical results of the two games are compared across several important dimensions: number of strategies available, number of iterations of the game, numbers of players, and the distribution of power among them. The discussion is illustrated with specific problems of international cooperation, and the implications of alternative cooperation problems for the formation and performance of international regimes are explored. The basic solutions for PD and coordination have divergent ramifications for the institutionalization, stability, and adaptability of regimes and for the role of hegemony in the international system. However, the coordination model does not replace the PD model but complements and supplements it as a way to understand the diversity of political institutions. These results are widely applicable to areas of politics beyond international relations.