The Breadth-Depth Trade-off and the Cost of Non-Cooperation in Multilateral Agreements


A common argument in the international relations literature is that multilateral agreements either set ambitious policies and include few states, or they include many states at the expense of lax policies. This conclusion derives from a simple model that captures an important aspect of multilateral agreements: the trade-off between breadth and depth. However, the focus on this trade-off overlooks the cost of staying out. In cooperation problems, such as climate change, in which the cost of non-cooperation increases over time, ignoring this cost renders our understanding of multilateral agreements incomplete. In my game-theoretic model, I capture this aspect by allowing countries, with heterogeneous ideal points, to also vary in their noncooperation cost. Substantively, variation in this cost parameter could come from countries’ higher exposure to negative externalities or domestic opposition to non-cooperation. In such a setup, I can show that broad treaties can be sustained even for deep commitments when staying out is expensive. This result has two important implications for IR scholarship and the breadth depth trade-off literature in particular. First, as the distribution of non-cooperation costs across countries differs by issue, the breadth-depth trade-off must necessarily be issue-specific, too—an insight that is currently overlooked. Second, empirical models of treaty participation that ignore non-cooperation cost are likely misspecified due to omitted variable bias.

Working paper. [PDF]