″...everyone’s utility in a given round … is the negative of the average temperature.” Why would we assume that?
”Clearly, this is feasible, because it’s happening.” Is this rational? Isn’t this synonymous with saying “clearly my scenario makes sense because my scenario says so”?
“Each prisoner’s min-max payoff is −99.3” If everyone else is min-maxing against any given individual, you would have a higher payoff if you set your dial to 0, no? The worst total payoff would be −99.
What am I missing? Can anyone bridge this specific gap for me?
“Feasible” is being used as a technical term-of-art, not a value judgment. It basically translates to “physically possible”. You can’t have an equilibrium of 101 because the dials only go up to 100, so 101 is not “feasible”.
The min-max payoff is −99.3 because the dials only go down to 30, not to 0.
We’re assuming that utility function because it’s a simple thought-experiment meant to illustrate a general principle, and assuming something more complicated would just make the illustration more complicated. It’s part of the premise of the thought-experiment, just like assuming that people are in cages with dials that go from 30 to 100 is part of the premise.
The problem is that the model is so stripped down it doesn’t illustrate the principle any more. The principle, as I understand it, is that there are certain “everyone does X” equilibria in which X doesn’t have to be useful or even good per se, it’s just something everyone’s agreed upon. That’s true, but only to a certain point. Past a certain degree of utter insanity and masochism, people start solving the coordination problem by reasonably assuming that no one else can actually want X, and may try rebellion. In the thermostat example, a turn in which simply two prisoners rebelled would be enough to get a lower temperature even if the others tried to punish them. At that point the process would snowball. It’s only “stable” to the minimum possible perturbation of a single person turning the knob to 30, and deciding it’s not worth it any more after one turn at a mere 0.3 C above the already torturous temperature of 99 C.
I’m confused. Are you saying that the example is bad because the utility function of “everyone wants to minimize the average temperature” is too simplified? If not, why is this being posted as a reply to this chain?
I’m in the same boat.
″...everyone’s utility in a given round … is the negative of the average temperature.” Why would we assume that?
”Clearly, this is feasible, because it’s happening.” Is this rational? Isn’t this synonymous with saying “clearly my scenario makes sense because my scenario says so”?
“Each prisoner’s min-max payoff is −99.3” If everyone else is min-maxing against any given individual, you would have a higher payoff if you set your dial to 0, no? The worst total payoff would be −99.
What am I missing? Can anyone bridge this specific gap for me?
“Feasible” is being used as a technical term-of-art, not a value judgment. It basically translates to “physically possible”. You can’t have an equilibrium of 101 because the dials only go up to 100, so 101 is not “feasible”.
The min-max payoff is −99.3 because the dials only go down to 30, not to 0.
We’re assuming that utility function because it’s a simple thought-experiment meant to illustrate a general principle, and assuming something more complicated would just make the illustration more complicated. It’s part of the premise of the thought-experiment, just like assuming that people are in cages with dials that go from 30 to 100 is part of the premise.
The problem is that the model is so stripped down it doesn’t illustrate the principle any more. The principle, as I understand it, is that there are certain “everyone does X” equilibria in which X doesn’t have to be useful or even good per se, it’s just something everyone’s agreed upon. That’s true, but only to a certain point. Past a certain degree of utter insanity and masochism, people start solving the coordination problem by reasonably assuming that no one else can actually want X, and may try rebellion. In the thermostat example, a turn in which simply two prisoners rebelled would be enough to get a lower temperature even if the others tried to punish them. At that point the process would snowball. It’s only “stable” to the minimum possible perturbation of a single person turning the knob to 30, and deciding it’s not worth it any more after one turn at a mere 0.3 C above the already torturous temperature of 99 C.
I’m confused. Are you saying that the example is bad because the utility function of “everyone wants to minimize the average temperature” is too simplified? If not, why is this being posted as a reply to this chain?