# A Reasonable Approximation

### Your Opponent Can Precommit Too

Chicken is a well-known two-player game in which the players get inside different cars, drive towards each other, and hope that the other player swerves out of the way. If both players swerve, they both lose small amounts of charisma. If one player swerves and the other doesn't, the swerver loses a slightly larger amount of charisma, and the non-swerver gains a small amount. If neither player swerves, both lose a large (occasionally fatal) amount of HP, and a small amount of charisma.

It is sometimes said[citation needed] that there is an optimal strategy to playing Chicken: after pointing your car at your opponent, remove your steering wheel. Now you can't swerve, so she knows that she can either swerve or crash.

Hearing this strategy, you head down to your local Chicken field, armed with your trusty screwdriver, and eager for a game. You quickly find an opponent. The two of you perform the traditional squaring-off ritual, enter your respective vehicles, and wheel around to face each other. You take your screwdriver in hand, smile sweetly at your opponent… and realise that she has had the same idea, and is already removing her steering wheel.

Are you still going to remove your own wheel? Or are you going to swerve?

It's easy to think that Chicken can turn into a game of "who can precommit first". We race to remove our steering wheels; if I win, then you have to swerve or crash, and if you win, then I have to swerve or crash.

But what if I put on a blindfold? Now if you remove your steering wheel, I won't know about it. What good does it do you then? Even if you always remove your steering wheel, assuming your opponent doesn't remove theirs first - and even if I know that you do that, and you know that I know, and so on - do I know that you're still going to do it when I can't see you do it? You'd like me to think that you will, but how do you convince me? And even if you do convince me, I can still remove my own steering wheel, and if I do it while blindfold I won't know if you beat me to it.

With a blindfold, I'm not precommiting not to swerve, although I can do that as well if I choose. I'm precommiting to ignore your precommitments. (Sort of. I'm precommiting not to receive any sensory input about your precommitments. I can still react to your precommitments, e.g. if both you and my model of you precommit despite me not seeing you do it.)

Of course, you can also put on a blindfold. So maybe we race to do that? But then I can tell you before the game that even if you put on a blindfold, I'm still removing my steering wheel. And you say there's no reason for me to do that, so you don't believe that I will. And I say, "try me". If I've said this in front of a large audience, the cost to me of swerving just went up. Moreso if some of the audience are potential future blindfold opponents.

And you can say the same thing to me. But this meta-level is different. If you've removed your steering wheel, you can't swerve. If you've blindfolded yourself, you can't see me precommit. Those are credible precommitments. There's no object-level reason for me to copy you after you've already done it. But just telling me of your precommitment is far less credible, you can always change your mind.

So if you tell me that you're going to ignore my precommitment to ignore your precommitment, I can tell you the same thing, hoping to change your mind.

Assuming neither of us claims to back down, what happens now? We face off against each other, and if I blindfold myself, I don't know whether you're going to do the same, and I don't know whether you're going to remove your steering wheel, and you know I don't know, and I know you know I don't know… and it seems to me that we're back at the original game.

(Incidentally, I've ignored the possibility that a steering wheel might be replaceable; or that a blindfold can be removed, or light enough to see through from the inside. These possibilities make your precommitments less credible.)

Posted on 07 December 2013

Tagged: game theory; rationality