April 4, 2006
A while ago I noticed a common feature of living with a roommate that reminded me of game theory, and determined to subject it to a poorly-informed analysis. Eight months or so later, here it is for your enjoyment. No, it's not brinksmanship, like when you put off cleaning the kitchen for so long that the roommate wants it done so badly he just does it himself--though I have plenty of experience with that game.
It happens all the time that roommates differ about a certain habit that affects the apartment. For example, we have a Brita filter/water jug. My roommate likes to keep it outside of the refrigerator so the water is at room temperature. I prefer it refrigerated. For a while I thought he was just leaving it out by accident, and every time I found it out, I would put it back in the fridge. Then the next time I went to get water, it would be out again. Eventually I realized that, give or take a few, every time I wanted water it was out, where I didn't want it, and every time my roommate wanted water, it was in the fridge where he didn't want it. So we were both losing out by trying to get what we wanted. I stopped putting the jug in the fridge and started keeping a good supply of ice cubes. Nothing was ever said about it.
In the Prisoner's Dilemma, if the prisoners try to rat each other out to get a more lenient sentence for themselves, they end up with the worst outcome because they're both caught lying. They're best off if they both cooperate and keep quiet because then the authorities get no proof. In the same way, assuming we take turns drinking water (which isn't perfectly true but tends to happen more often than not), we would actually be best off if I took the water out of the fridge, and my roommate put it in, doing the opposite of what we each want to do. I think this would require some discussion to get going, and might not be possible.
The main difference seems to be that while the Prisoner's Dilemma has both one-time and iterated forms (in the latter the prisoners play again and again and try to end up with the best overall score, having a chance to react to the other's actions), the roommate's dilemma seems to evolve from an iterative structure. And that's about as far as I can take it.