Game Theory and Foreign Policy

Consider the following "battle of the sexes" game, one of the only things I remember from my game theory class. A boyfriend and girlfriend are not allowed to communicate, and both face the choice between going to the football game or the movies. When making the choice simultaneously, neither knows what the other is going to do, but each formulates a best response, which is the strategy that maximizes his/her satisfaction given the action that he/she anticipates the other will choose. Now being together at either event is considered by both to be superior to being apart. Thus, if the guy knows that the girl prefers football, and the girl knows that the guy prefers football, naturally each will choose to go to the football game. But if the girlfriend prefers the movies, and the boyfriend the football game, the best response becomes more difficult for each.

Depending upon how you set the "payoffs," the best response for each might be to flip a coin in order to decide, playing what is called a mixed (as opposed to a pure) strategy. In fact, that turns out to be the only Nash equilibrium (named for John Nash of a A Beautiful Mind fame), defined as a vector of strategies for the two players where each individual strategy is a best response to the strategy of the other player. Now here is where it gets interesting: there is a 50 percent chance, not insignificant, that the two show up at different events, and moreover there is a 25 percent chance that the guy shoes up at a chick-flick, while the lady shows up at the football game, an outcome that defines the worst case scenario for both players.

Now the point of this little lesson relates to the situation in Iraq, or at least it might. It is possible that a bad outcome comes from an entirely correct strategy, and even that such a possibility has a fairly high likelihood of occurring. The pre-history of the D-Day invasion, for example, involved every effort of the allies to cloak their true target - Normandy - and feign toward somehwere else in hopes that the key German defenses would prepare in the wrong spot. And that is exactly what happened.

The German's might have had enough intelligence to suggest that there was a 50/50 chance of the Normandy invasion versus what turned out to be the fake alternative. Splitting their forces evenly between the two places may have been a sure-fire losing strategy no matter where the Allies landed. So the Nash equilibrium response for the Germans may have been to flip a coin, and send 75 percent of their troops one place, and the remainder to the other. An unlucky coin flip may have been the determinant of the Allies success. Again, that may have truly been the best strategy, but it obviously turned out badly for the Germans.

But after such a failure, the knowledge of where the Allies actually landed - Normandy - distorts everyone's perception of what the Germans should have done. The German strategy may have been formulated by culling the advice of many in their intelligence operations, each with opinions that no doubt varied as to where the true threat lay. Maybe one such operative thought with certainty that Normandy was the place - and he may have truly been wrong about that (especially if the Allies actually flipped a coin to decide at the last minute). But after the fact, and especially before the Germans had any knowledge of the true strategy of the Allies, it will appear that the decision makers made a mistake in ignoring the advice of the guy who kept screaming about Normandy. If Germany had a 60 Minutes, and a free press that was adversarial to Hitler, you could bet that the guy who was certain about Normandy would be given a platform on the show to spin his newly released book, a la Richard Clarke.

The point is this - to the press, the fact that the girlfriend showed up at the football game becomes, ex post, the only prediction they consider to be reasonable at the time the boyfriend had to make the decision. If the boyfriend was being advised by a bad game theorist, the press has someone there to say that the boyfriend ignored the correct advice. But that, of course, is not true. In this case, it is not true to say that the press is necessarily biased, but their lack of nuance makes them unable to see that a guy who appears to be correct ex post may have been completely wrong ex ante. In more bluntly stupid variations of this "bias", a reporter might suggest that one memo among reams of intelligence data that suggested terrorist flying planes into buildings should have been heeded to the point of providing military protection to obvious targets.

War is filled with strategic decisions made under uncertainty. Like the separate boyfriend and girlfriend, or the Germans stationed at the wrong beach, bad outcomes are not always the result of bad decisions. Assessing decisions made in the course of war is inherently a very speculative venture, and it is compounded by the fact that information that is classified may otherwise exonerate the decision makers as being rational, but they are prevented from using it in their own defense. The set of what is known to the talking heads is usually only a subset, and probably a small one at that, of the information available to the actual decision makers.

This is why people can tell me that Bush screwed up in Iraq until the cows come home, and I just don't buy it. I think Bush has a very talented and intelligent cabinet, and I think the military is led by similarly talented and intelligent people. I trust that, even as I know that others do not. But I recognize, unlike them, that given my knowledge set, I can't really prove my gut. But my inability to prove that a bad result in Iraq is nevertheless a possible outcome of a good decision is no proof that it is necessarily the outcome of a bad decision.