Walking is Difficult

Hello everybody!

For this very first post, I thought I'd provide an example of a situation that might warrant some game theoretic analysis. I often walk places, which is a thing that quite a few people seem to do.  This means that sometimes other people end up walking straight toward me.  I don't want to bump into them, they don't want to bump into me.  The following game is an example of that situation

		P2
		Turn	Straight
P1	Turn	1,1	1,2
	Straight	2,1	0,0

Here it doesn't really matter whether I'm Player 1 or Player 2, as their preferences are symmetrical.  Neither person knows what the other will choose, but they do know what outcome they want.

When we look at the pure strategy equilibrium of this game, it's best for the players to play different strategies.    Put another way, if you pick Turn, I should pick Straight.  If you pick Straight, I should pick Turn.  To anybody who's faced this situation, this result is fairly obvious.

However, determining who ought to turn is a rather more difficult endeavor.  Without knowing what you're inclined to do, I might decide to go straight, since I know that you know that turning is better than a collision.  If we both think this, we'll shortly perform a rather awkward sort of dance.

You might be inclined to ask:  Michael, even if I know this, what should I do when I find myself in this situation?

Clearly the best thing to do is for you to always turn.  That way, I'll never have to worry about running into anyone.