I set the dial to 30 and don’t change it no matter what.
In the second round, temperature lowers to 98.3.
In the third round all the silly people except me push the dial to 100 and thus we get 99.3.
I don’t deviate from 30, no matter how many rounds of 99.3 be there.
At some point someone figures out that I am not going to deviate and they defect too, now we have 88.6.
The avalanche has started. It won’t take long to get to 30.
Now, this was a perfectly rational course of action for me. I knew that I will suffer temporarily, but in exchange I got a comfortable temperature for eternity.
Looking ahead multiple moves seems sufficient to break the equilibrium, but for the started assumption that the other players also have deeply flawed models of your behavior that assume you’re using a different strategy—the shared one including punishment.
There does seem to be something fishy/circular about baking an assumption about other players strategy into the player’s own strategy and omitting any ability to update.
Count me in : )
If we assume that there are at least two not-completely-irrational agents, you are right. And in case there aren’t, I don’t think the scenario qualifies as a “game” theory. It’s just a boring personal hell with 99 unconscious zombies. But given the negligible effect of punishment, I’d rather keep my dial at 30 just to keep the hope alive, than surrendering to the “policy”.
Of course it is perfectly rational to do so, but only from a wider context. From the context of the equilibrium it isn’t. The rationality your example is found because you are able to adjudicate your lifetime and the game is given in 10 second intervals. Suppose you don’t know how long you have to live, or, in fact, now that you only have 30 seconden more to live. What would you choose?
This information is not given by the game, even though it impacts the decision, since the given game does rely on real-world equivalency to give it weight and impact.
I am quite confused what the statement actually is. I don’t buy the argument about game ending in 30 seconds. The article quite clearly implies that it will last forever. If we are not playing a repeated game here, then none of this makes senses and all the (rational) players would turn the knob immediately to 30. You can induct from the last move to prove that.
If we are playing a finite game that has a probability p of ending in any given turn, it shouldn’t change much either.
I also don’t understand the argument about “context of equilibrium”.
I guess it would be helpful to formalize the statement you are trying to state.
I don’t think this works. Here is my strategy:
I set the dial to 30 and don’t change it no matter what.
In the second round, temperature lowers to 98.3.
In the third round all the silly people except me push the dial to 100 and thus we get 99.3.
I don’t deviate from 30, no matter how many rounds of 99.3 be there.
At some point someone figures out that I am not going to deviate and they defect too, now we have 88.6.
The avalanche has started. It won’t take long to get to 30.
Now, this was a perfectly rational course of action for me. I knew that I will suffer temporarily, but in exchange I got a comfortable temperature for eternity.
Prove me wrong.
Looking ahead multiple moves seems sufficient to break the equilibrium, but for the started assumption that the other players also have deeply flawed models of your behavior that assume you’re using a different strategy—the shared one including punishment. There does seem to be something fishy/circular about baking an assumption about other players strategy into the player’s own strategy and omitting any ability to update.
Count me in : ) If we assume that there are at least two not-completely-irrational agents, you are right. And in case there aren’t, I don’t think the scenario qualifies as a “game” theory. It’s just a boring personal hell with 99 unconscious zombies. But given the negligible effect of punishment, I’d rather keep my dial at 30 just to keep the hope alive, than surrendering to the “policy”.
Of course it is perfectly rational to do so, but only from a wider context. From the context of the equilibrium it isn’t. The rationality your example is found because you are able to adjudicate your lifetime and the game is given in 10 second intervals. Suppose you don’t know how long you have to live, or, in fact, now that you only have 30 seconden more to live. What would you choose?
This information is not given by the game, even though it impacts the decision, since the given game does rely on real-world equivalency to give it weight and impact.
I am quite confused what the statement actually is. I don’t buy the argument about game ending in 30 seconds. The article quite clearly implies that it will last forever. If we are not playing a repeated game here, then none of this makes senses and all the (rational) players would turn the knob immediately to 30. You can induct from the last move to prove that.
If we are playing a finite game that has a probability p of ending in any given turn, it shouldn’t change much either.
I also don’t understand the argument about “context of equilibrium”.
I guess it would be helpful to formalize the statement you are trying to state.