World War I in Real Time: First Edition Problems

I’m teaching out of my World War I game theory textbook for the first time this semester, and as I worked through some early-morning class prep this morning, I noticed a tiny little error in Chapter 2. But worry not: all the equilibria still exist, and for the same reasons. It’s a typo, but one worth clarifying.

What’s the issue?

Section 2.2, “Commitment Problems and War,” motivates a game in which state A has to decide whether to launch a preventive war in light of the possibility that B, who’s rising in strength, might renege on the status quo in the future. And in describing A’s payoffs, I say that its best outcome of a peacefully honored status quo gives it 4, its worst outcome of passing on war only to see the status quo renegotiated is 1, and the middling outcome of launching a preventive war today is 2. That’s true whatever B’s strategy happens to be, because that strategy is preempted by A’s use of war.

That … makes sense.

But for some reason, in Figure 2.5 (rendered below), A gets 2 for the outcome of the (attack; honor) strategy profile and 3 for the (attack; renege) strategy profile. That’s…unnecessary. A should really get 2 for both, unless we want to say that attacking a B that would’ve honored the agreement is regrettable, but that’s not necessary for the story. It’s also not in my initial description of the payoffs.

Screen Shot 2020-01-30 at 5.39.22 AM

Now, as you’ll see, the Nash Equilibrium of the game (marked by the solid gray lines) is the same whether that offending 3 is in there or is replaced by the intended 2:

Screen Shot 2020-01-30 at 5.50.08 AM

But I don’t want to let errors like this pass without some kind of note to adopters and students and whoever else has posts on this blog inflicted on them.┬áSo, apologies, dear reader(s). Let’s hope there aren’t too many more posts like this one forthcoming.

My own buffoonery aside, there’s a useful point here: forcing ourselves to “do the math” means we can more easily find, correct, and assess the consequences of mistakes in our premises and/or our reasoning. That’s always and everywhere a good thing for the social scientist.