At this late stage in the occupation of Iraq, many of Henry Kissinger’s old arguments about Indo-China are being dusted down. One of the hoariest and worst is that we need to “stay the course” (or some similar euphemism) in order to maintain “credibility” – to demonstrate our resolve to our enemies, who will otherwise continue to attack us. It reminds me of my one and only contribution to the corpus of game theory.
The Folk Theorem in game theory states that any outcome of a repeated game can be sustained as an equilibrium if the minimax condition for both players is satisfied. In plain language, it can be summarised as stating that “if we take strategic considerations into account, there is a game-theoretic rationale for practically anything”. This formulation leads on to my contribution, the Davies-Folk Theorem, which states that “if we take strategic considerations into account,there is a game-theoretic rationale for practically fucking anything” (it’s a fairly simple corollorary; proof available from author on request).
The point being that since game theory in general provides the analyst with so many opportunities to twist himself repeatedly up his own arse like a berserk Klein bottle, if a given real-world course of action appears to have nothing going for it other than a game-theoretic or strategic justification, it’s almost certainly a bad idea. Thus it is with that bastard child of deterrence, “credibility”.
Here’s a fine example of the problem, via Matthew Yglesias; although the guy tries to present it as an argument against the economists, the concept of “military strategy” he is talking about here comes directly from Thomas Schelling. The idea is that the war is costing huge amounts of money and lives with no real prospect of success and a distinct danger that it is making things much worse. However, to do the logical thing would send the signal to our enemies that we will give up if fought to a pointless bloody standstill. Therefore, for strategic reasons, we must redouble our efforts, in order to send the signal to our enemies that we will fight implacably and mindlessly in any battle we happen to get into, forever, in order to dissuade them from attacking us in the first place. It’s got the kind of combination of “counter-intuitive” thinking and political convenience that always appeals to the armchair Machiavelli, as well as to the kind of person who thinks it’s witty to describe things as “Economics 101”(Airmiles has been all over this one for ages, naturally). What’s it like as a piece of game-theoretic reasoning?
Lousy. It is certainly true that one of the benefits of doing something stupid is that it saves you from having to spend money on maintaining your reputation as an idiot. However, is the reputation of an idiot really worth having?
It turns out that it can be proved by theorem that the answer is no. If the game of being a belligerent idiot with no sensible regard for one’s own welfare was worth the candle, in the sense of conferring benefits which outweighed the cost of gaining it, then everyone would want to get that reputation, whether they were genuinely an idiot or not. But if everyone wanted that reputation, then everyone would know that simply acting like an idiot didn’t mean that you were one, in which case it would be impossible to establish a reputation as an idiot in the first place. The point here is that it’s one of the more important things in game theory that a signal has to be a costly signal to be credible; like membership of the Modern Languages Association, a reputation in deterrence theory is something that is worth having, but not worth getting. People who use the word “signal” in this context (usually on the basis of a poorly understood or second-hand reading of Schelling) don’t always seem to realise that they are explicitly admitting that the costs of being in Iraq are greater than the benefits.
Because of this, in my opinion it is very difficult for a democracy to establish this kind of credibility. The reason is that although leaders are often idiots, democratic polities rarely are. It is very hard for a democratically elected leader to credibly commit to a policy of stupidity, because everyone else knows that it is highly likely that the electorate will not support it. I hasten to add that to take this obvious fact and turn it into a Dolchstosslegende, or to bemoan the lack of national vigour in the manner of Victor Davis Hanson is to get the analysis back to front. It is a good thing about democracies that they don’t in general do stupid things, and the fact that an argument from “credibility” and “deterrence” can be constructed to make the case that it is a weakness (even “a fatal weakness”) of democracies that they are insufficiently inclined to pointless military dead-endism is just another example of the Davies-Folk Theorem. Here’s the same point made by someone else if you like it dressed up in numbers and 2×2 boxes.
Furthermore, even if we were to accept this bogus argument, it is worth remembering that it is of rather general application. As the marketers will tell you, delivery has to be consistent with the brand; you can’t tell people to ignore part of your message. If it were true that by sticking it out past the bitter end,we were signalling that we were bitter-enders, then what othermessages might we have been sending out over the last few years? In particular, what message does our behaviour since 2003 convey on such important topics as: whether or not we want to fight a war against theIslamic ummah? Or whether the best way to protect yourself against us invading you is to get nuclear weapons? Or whether we are reliable allies? Whether our public statements to the United Nations can be trusted? When you start thinking in these terms, you start really worrying about the reputation that we are actually getting.