Annals of Game Theory: Deterrence, Signaling, and Idiocy

The two correct and useful applications of game theory to strategy that I know I learned from Nena and from Daniel Davies:

Daniel Davies: 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”....

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.”...

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... [would maintain] your reputation as an idiot. However, is the reputation of an idiot really worth having?... [N]o. If... being [thought] a belligerent idiot... was worth [it]... then everyone would want to get that reputation... [and] simply acting like an idiot [wouldn't] mean that you were one, in which case it would be impossible to establish a reputation as an idiot....

The point here is that... in game theory... a signal has to be a costly signal... a reputation in deterrence theory is something that is worth having, but not worth getting. People who use the word “signal”... don’t... realise that they are explicitly admitting that the costs... are greater than the benefits....

[Thus] it is very difficult for a democracy to establish this kind of credibility.... [A]lthough 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....

Furthermore... 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 other messages 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 the Islamic 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.