The main defining feature of the international system is anarchy. There is no world government. And ours is not an imperial world. No country today, not even the United States, directly controls the foreign or domestic policies of other states. When states cooperate, they do so in the absence of a formal governing authority to mediate their interests and enforce agreement. Despite the emergence of a decentralized system in which states are not formally subservient to each other or any other entity, a plethora of international institutions exists to organize states. Why do these institutions, or “regimes”, exist? Who benefits, and to what extent; who bears the cost, and to what extent?

In this chapter, I provide some answers based on a plausible model of interactions among one large state and several smaller states. I turn first to conventional explanations for the emergence of international institutions (as well as interaction within them). In this section, I also examine gains allocation and the neorealist challenge, identifying problems with both the neoliberal and neorealist account of international institutions. Second, I review how size and public goods have been analyzed in the literature. Third, I briefly outline how one might model international cooperation in the context of a hegemonic power. The proposed model is a revised version of Duncan Snidal's size model and I justify why this is a suitable starting point for considering gains allocation and why modifications are needed in order to do so.