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.
Comments (7)
this is really just a zero sum game. there is no cooperative arrangement that could make you both better off. he either has his tepid water or you have your cold water at the exclusion of him having his tepid water.
April 4, 2006 8:05 AM
the problem is there is no middle ground on this issue. we would think of this as a "territorial issue" in international negotiation where you are currently in a state of conflict with your roommate where neither of you is really getting what you want, but only one of you can get what you want. You have two options to solve this:
1. Issue Linkage: You can,
a) commence a violent harrassment campaign against Peter, and agree to stop only as long as he agrees to keep the water in the fridge.
b) concede on some other issue you are conflicting over in exchange for him conceding on this issue.
or
2. Make a side payment: Give him something of value in exchange for your cold water. This could include buying him his own water jug.
April 4, 2006 8:23 AM
that was really 3 options
April 4, 2006 8:23 AM
Many thanks for your insightful and thorough analysis. But I don't understand why it's a zero-sum game. I suggested the solution that every time I take a drink, I leave the water out of the fridge afterward, and every time my roommate does so, he puts it back in the fridge. Then I always find it in the fridge and he always finds it out.
This includes the simplifying assumptions that we take turns drinking, and that there is enough time between turns for the water to become cold and to become tepid. Perhaps I should have laid those out more clearly.
But this way, by each doing what the other would like us to do, we both get what we want, no?
April 5, 2006 1:11 AM
in my analysis (and i will be sending the bill later today) i assume that it is your preference to have your cold water and as much cold water as you want exactly when you want. The arrangement you propose would allow the water to be cold half the time. In other words, half of the water would be cold if we hold time constant (though not half-cold which would be clearly undesirable, but a potential outcome of your arrangement). As I see it, this arrangement:
A) Requires additional effort and energy to maintain
B) Does not allow you complete freedom of action vis-a-vis your water
C) May not result in having water that is cold half the time, but half-cold most of the time.
If we ignore the costs of points A and C, and focus on the costs of point B and assume that the benefit is cold water half the time, then yes, this would be a prisoner's dilemma scenerio where there would be a temptation for you to keep the water in the fridge to enhance your accessability to the supply of cold water to the cost of Peter not having any water.
April 6, 2006 10:18 AM
i'm not sure it I can wrap my mind around jv's analysis, but I can attest to your expertise at brinksmanship. thanks for settling a long held suspicion. hope you're well j.
April 6, 2006 2:13 PM
there should be land for isreal & palestine.
April 8, 2006 10:28 AM