The analysis of spatial models in chapter 3 left us without a way to think about strategic behavior. Spatial models generally assume that everyone acts on his or her preferences in a sincere manner. The concept of subgame perfect Nash equilibrium, however, alerts us that adopting sincere behavior at each step in a decision process can lead to an inferior outcome for a decision maker. Instead, decision makers have strong incentives to be strategic. They choose their actions by taking their preferences into account to be sure. But they also consider the constraints they operate under, such as how much power they have compared to a rival, how confident they are about what their rival really wants, and how willing they are to take risks in pursuit of the policy results they desire. We have seen that game theory can be a very useful tool for sorting out the complex¬ity of international interactions and that it can be useful in informing policy choices and in predicting what actions people are likely to take and what offers they are likely to make to try to resolve problems. These issues are the essence of international affairs.

The rest of this book applies the tools introduced here to situations involving conflict and situations involving cooperation in international relations. The objective is to elucidate why things work the way they do and also to facilitate our ability to predict what is likely to happen in specific situations and develop the skills and knowledge to provide useful advice to leaders charged with the responsibility for making life and death decisions in the international arena.