Game Theory

Game Theory. Within national security analysis, Game theory deals with parties making choices that influence each other's interests, where they all know that they are making such choices. Using mathematics, it analyzes the think/doublethink logic of how each adversary sees the other, sees the other's view of it, and so on. Unlike war gaming, where real players assume roles, it involves only mathematical calculations.

John von Neumann and Oskar Morgenstern laid the foundation of game theory in the 1940s. Its application to military problems has been limited but interesting. One World War II example involved submarine warfare. A submarine is passing through a corridor patrolled by submarine‐hunting planes. The submarine must spend some time traveling on the surface to recharge its batteries. The corridor widens and narrows, and the submarine is easier to detect in the narrower parts, with less sea for the hunters to scan. Where should the submarine surface? Where should the hunters focus their effort? The premise that the wide part is the one logical place is self‐refuting. If it were true, the hunters would deduce that, would head there and leave the narrower part alone, making the narrower part better. Choosing the narrow part likewise leads to a contradiction. Game theory advises a “mixed” strategy—do one or the other unpredictably, using exact probabilities calculated from the ease of detection in each section.

Other applications have addressed the problems of when an interceptor aircraft closing on a bomber should open fire, how to allocate antimissile defenses to targets of varying value, and when to fire intercontinental missiles to avoid Soviet nuclear explosions in the stratosphere.

These problems involved specific wartime encounters. Another area is broad strategy. A prevalent misconception is that game theory set the principles of nuclear strategy. In the 1940s, planners hoped that the new mathematics would do this, but strategic problems proved too complex. It was hard even to specify each side's goals. Game theory has not given exact strategic advice, but it has clarified general principles. In a model of crisis confrontation, for example, one side wants to show the adversary that it values winning very highly, to induce the other side to back down. It uses the tactic of sacrifice‐to‐show‐resolve—make some costly military deployment so the adversary will conclude that only a determined government would pay such a cost to prove its determination. The model precisely illustrates the skeletal structure of strategic concepts such as showing resolve or enhancing credibility. By the 1990s, a sophisticated body of academic work had addressed deterrence, escalation, war alliances, and the verification of arms treaties.
[See also Disciplinary Views of War: Political Science and International Relations; Operations Research; Strategy; War Plans.]

Bibliography

Melvin Dresher , Games of Strategy: Theory and Applications, 1961.
Barry O'Neill , A Survey of Game Theory Studies of Peace and War, in Robert Aumann and Sergiu Hart, eds., Handbook of Game Theory, 1994.

Barry O'Neill