October 12, 2005

Schelling vs. Prince Hal

Discussing the latest Nobel Prize winners, Michael Mandel says that game theory is mostly pointless because it can't do what any good theory should be able to do—make testable predictions:
Game theory is no doubt wonderful for telling stories. However, it flunks the main test of any scientific theory: The ability to make empirically testable predictions. In most real-life situations, many different outcomes -- from full cooperation to near-disastrous conflict -- are consistent with the game-theory version of rationality.

To put it a different way: If the world had been blown up during the Cuban Missile Crisis of 1962, game theorists could have explained that as an unfortunate outcome -- but one that was just as rational as what actually happened. Similarly, an industry that collapses into run-amok competition, like the airlines, can be explained rationally by game theorists as easily as one where cooperation is the norm.
On the contrary! There has been at least one testable prediction generated by game theory, from Shakespeare's Henry V, when the king gives orders to slaughter all the French prisoners in English captivity:
But, hark! what new alarum is this same?
The French have reinforced their scatter'd men:
Then every soldier kill his prisoners:
Give the word through.
John Sutherland thought this scene makes Henry a war criminal, and indeed it does, but at least one other critic (I forget who, William Empson maybe) noted the strategic logic behind all of this: Henry had all the French prisoners killed in sight of the French army, so that all the English soldiers knew the French knew, and would then assume that the French would kill them if they lost the battle and were taken prisoner. Right? Henry was just giving the English incentive not to surrender. And they ended up defeating the much larger French army at Agincourt, so his theory panned out.

No, seriously, I don't know anything about this. But Mandel's seems right when he says that "real-world decision-makers frequently appear not to evaluate uncertain events according to the laws of probability." Take our president! He doesn't appear to be in the grips of any rational theory of deterrence. So, for instance, the Pentagon recently floated moronic plans for pre-emptive nuclear strikes on nations in danger of using WMDs—thus knocking the theory of deterrence on its ass and making an attack on the United States more rather than less likely. (Since, if rogue nations face the threat of pre-emptive rather than retaliatory strikes, they have less incentive to avoid attacking.) And Bush clearly didn't believe that Iraq could be deterred, right? But wait! During the initial phase of the 2003 invasion, the administration promised unspecified retaliation against Iraqi generals if they used WMDs. (See, for instance, this story.) Wha—? So deterrence does work... More likely, the entire system breaks down once you have someone who doesn't believe in any of it.
-- Brad Plumer 12:50 PM || ||