Why was the Moroccan Crisis resolved peacefully, while the July Crisis ended in World War I? Why did Soviet Premier Nikita Khrushchev choose to put missiles in Cuba, setting the stage for the Missile Crisis, and why were Khrushchev and President Kennedy able to end that crisis short of war? What factors increase or decrease the stability of nuclear deterrence? Diplomacy, broadly construed, is of the utmost importance to whether countries escalate their disputes to crises and their crises to wars. Frank C. Zagare’s welcome new book presents answers to these and other questions about diplomatic history and security studies using game-theoretic models. In doing so, it makes a case for the use of game theory, and more particularly for the use of analytic narratives, in the study of diplomatic history and security studies.

The book consists of three sections. The first is an overview that briefly introduces basic concepts of game theory and the idea of an analytic narrative. It discusses model selection, equilibrium selection, and choosing appropriate assumptions about actors’ preferences, topics that recur through the book.

The second and analytically central section of the book consists of three such narratives that apply “off-the-shelf” game-theoretic models to explain the unfolding of the Moroccan Crisis of 1905–1906, the Cuban Missile Crisis, and the start of World War I. The final section of the book uses what Zagare calls “perfect deterrence theory,” a group of game-theoretic models developed with Marc Kilgour, to understand two general topics in international relations, deterrence and the Long Peace between the United States and the Soviet Union (Perfect Deterrence, 2000).

Zagare’s book is a rich argument in favor of a set of his earlier models, in addition to an argument in favor of the use of game theory and of analytic narratives in general. He has been using game-theoretic models to study international security for about four decades, and he draws from his well-developed body of work when choosing models to apply to the topics at hand. While the book’s abstract arguments in favor of game theory are fairly standard, these points come to life in the “argument-by-example” in the second and third sections. The book argues that game-theoretic explanations are “more transparent and less ad hoc” than explanations that are less theoretical (p. 2). The second and third sections, particularly the analytic narratives, meticulously show the reader what the book means by “less ad hoc” as it justifies the choice of model and by “transparent” as it explicitly states and justifies its assumptions. The fact that Zagare’s game-theoretic models present reasonable explanations of important aspects of the Moroccan Crisis, the Cuban Missile Crisis, and the start of World War I and can increase understanding of nuclear deterrence and the Long Peace is important evidence in favor of their usefulness. If an expert on a crisis disagrees with Zagare’s explanation, the book’s careful discussion of assumptions should allow them to pinpoint their areas of disagreement.

Some parts of the book would be a good choice for upper-level undergraduate as well as graduate classes in security studies or game theory, if supplemented with some instruction in game theory itself. Both the cases and the deterrence topics are substantively interesting examples that can motivate the use of game theoretic models in the study of international relations. Zagare’s detailed explanations of his choices also makes the book a useful “how-to” for people new to the idea of applying a model to explain a case. Some parts of the book explore esoteric concepts, however; for example, the first of two chapters on the Cuban Missile Crisis contains an extensive discussion of the theory of metagames.

While the book frames itself as, at least in part, an argument in favor of “analytic narratives,” it is not crystal-clear about what it means by the term. The approach was developed by Robert H. Bates et. al. (e.g., Analytic Narratives, 1998). The version in this book uses game-theoretic models to understand particular historical cases, and in doing so to evaluate the usefulness of the models. Yet many works in the literature on international security combine game theoretic models with case studies for one or both of these same two purposes without using the term “analytic narratives” (see, e.g., another game-theoretic explanation of the July Crisis: Alexandre Debs, “Mutual Optimism and War, and the Strategic Tensions of the July Crisis,” American Journal of Political Science 66[2022]: 271-284). It would have been interesting to hear Zagare’s thoughts about the strengths and weaknesses of this alternative compared to other, similar approaches.

Another limitation of the book is that it does not tackle many of the thornier issues related to the development or choice of game theoretic models. One such issue is whether a game-theoretic model—or, indeed, any model—should, in the abstract, be able to explain any one historical case. Because there are few if any laws in the social sciences, social-science data always are scattered around a regression line, even when the statistical model is a good representation of good theory. Most of the time, the scatter, or error, comes from a number of unmodeled factors, rather than one or two. Moreover, game-theoretic models are typically quite simple; a model illuminates at most a few important aspects of a phenomenon. Scholars are aware that many additional facets of a situation besides the one(s) on which their model focuses affect the case (or even the phenomenon). Thus, on average, there should be considerable “scatter” around the explanation offered by a good game-theoretic model. Identifying all of the important unmodeled factors that constitute this theoretical error in a particular case is difficult, so that, in the abstract, the error should make it difficult to see the mechanism of the theory operating in many of the cases. This line of thinking reveals a conundrum: models are useful because they explain an important phenomenon, but it should be difficult to show that they do so for any one data point or case. One answer to the problem is statistical work, though such work has its own limitations.

Of course, the combination of game-theoretic models and historical cases is extremely common, and often compelling in practice. As Zagare’s book illustrates, a well-chosen game-theoretic model adds clarity and precision to any argument about the factors at play in a given case. Beyond this book, in-depth study of historical cases also can be useful for developing and refining models.

Overall, then, Game Theory, Diplomatic History, and Security Studies is a practical demonstration of the use and usefulness of game theory to understand crisis diplomacy and security. This useful demonstration serves as a synthesis of and addition to a portion of Zagare’s prior work.