Game theory in diplomatic history: The basics
Known as the science of strategy, game theory is a branch of mathematics that has gained broad acceptance as a legitimate methodological tool. In this adapted excerpt from Game Theory, Diplomatic History and Security Studies, Frank Zagare explains the basic concepts behind the application of game theory in the fields of security studies and diplomatic history.
Game theory is the science of interactive decision making. It was created in one fell swoop with the publication of John von Neumann and Oskar Morgenstern’s Games and Economic Behavior (1944). The basic concept is that of a game itself.
A game can be thought of as any situation in which the outcome depends on the choices of two or more decision makers.
The term is somewhat unfortunate: games are often thought of as lighthearted diversions, but in game theory the term is not so restricted. For instance, most if not all interstate conflicts qualify as very serious games, including, but not limited to, trade negotiations, acute crises, and all-out wars.
In game theory, decision makers are called players. Players can be individuals or groups of individuals who, in some sense, operate as a coherent unit. Presidents, prime ministers, kings and queens, dictators, foreign secretaries, and so on can therefore sometimes be considered as players in a game. But so can the states in whose name they make foreign policy decisions. It is even possible to consider a coalition of two or more states as a player. For example, in their analysis of the July Crisis of 1914, Snyder and Diesing (1977) use elementary game theory to examine the interaction between “Russia–France” and “Austria–Germany.”
The decisions that players make eventually lead to an outcome, and in game theory an outcome can be just about anything.
Thus, the empirical content associated with an outcome will vary depending on the game being analyzed. Sometimes, generic terms such as “compromise” or “conflict” are used to portray outcomes. At other times, the descriptors are much more specific. Snyder and Diesing use the label “Control of Serbia” by Austria–Germany to partially describe one potential outcome of the July Crisis, for example.
Reflecting perhaps the intensity of the Cold War period in the United States in the early 1950s, almost all of the early applications of game theory in the field of security studies analyzed interstate conflicts as zero-sum games. A zero-sum game is any game in which the interests of the players are diametrically opposed. In a zero-sum game, what one player wins, the other loses. Examples of this genre include an analysis of two World War II battles by O. G. Haywood (1954) and a study of military strategy by McDonald and Tukey (1949).
By contrast, a nonzero-sum game is an interactive situation in which the players have mixed motives. That is, in addition to conflicting interests, they may also have some interests in common. Two states locked in an economic conflict, for instance, obviously have an interest in securing the best possible terms of trade. At the same time, they both may also want to avoid the costs associated with a trade war. It is clear that, in such instances, the interests of the two states are not diametrically opposed.
Payoffs are measured by a utility scale. Sometimes only ordinal utilities are, or need be, assumed. Ordinal utilities convey information about a player’s relative ranking of the outcomes. In many studies of interstate conflict, however, cardinal utilities are assumed. A cardinal scale indicates both rank and intensity of preference. In game theory, the players are assumed to be instrumentally rational. Rational players are those who maximize their utility. Utility, though, is a subjective concept. It indicates the worth of an outcome to a particular player. Since different players may evaluate the same outcome differently, the rationality assumption is simply another way of saying that the players are purposeful, that is, that they are pursuing goals (or interests) that they themselves define.
Rationality, however, does not require that the players are necessarily intelligent in setting their goals.
It may sometimes be the case that the players are woefully misinformed about the world and, as a consequence, have totally unreasonable objectives. Still, as long as they are purposeful and act to bring about their goals, they can be said to be instrumentally rational.
The second part of our series on game theory puts these features of the theory into practice when analysing the Rhineland Crisis of 1936.
Frank C. Zagare is UB Distinguished Professor of Political Science at the University at Buffalo, The State University of New York (SUNY). Professor Zagare’s main research interests lie in the nexus between security studies and game theory. He is the author of Game Theory, Diplomatic History and Security Studies (OUP, 2018).
