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Author | Topic: Test your wits | |||||||||||||||||||||||
AZPaul3 Member Posts: 8513 From: Phoenix Joined: Member Rating: 5.2 |
what colour was he? White. Though he was wearing a red Tam O'shay.
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AZPaul3 Member Posts: 8513 From: Phoenix Joined: Member Rating: 5.2 |
What temperature is it? Interesting. I like this. Quite hot, I imagine, but two questions: A. What is the range of the thermometer? 2. Was he wearing a red Tam O'shay?
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Hyroglyphx Inactive Member |
Well, you guys figured it out. Indeed, it is the "Prisoners Dilemma" and the "Kavka's Toxin Puzzle." Most of you got the first one; that the principle Professor Nash advocated -- that cooperation wins out over self-interest.
Kavka's Puzzle, however, really has no right or wrong answer. It is supposed to lead into a metaphysical or theological question about predestination or freewill. The basic premise is this: Can you intend to drink the toxin, if you know you don't have to? The object of the exercise isn't really about how you get the money, the point of the exercise is to parallel the theological question of freewill vs predestination. You all did very well, and some of your answer were very clever. I was interested in seeing your rationale. “Tu ne cede malis sed contra audentior ito" |
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Rrhain Member Posts: 6351 From: San Diego, CA, USA Joined: |
Modulous writes:
quote: Incorrect. If you keep silent and they also do, you only get six months. If you betray and they also do, you get five years. It is better to keep silent. This is an old puzzle. If you want, I can go through the math.... Rrhain Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.
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Rrhain Member Posts: 6351 From: San Diego, CA, USA Joined: |
LucyTheApe asks:
quote: Not to spoil it:
White as the only way you can walk 4 km south, 6 km east, and then 4 km north to wind up exactly where you started again is if you were at the North Pole. As the only bears up there are polar bears (assuming no artificially transported bears), that would mean you shot a white bear. Rrhain Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.
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Modulous Member Posts: 7801 From: Manchester, UK Joined: |
If you want, I can go through the math I'd really like to see your working.
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LucyTheApe Inactive Member |
Modulous writes: What temperature is it? It's about 22oC or 295.15K or 71.6F here, butthat's because I've got the heater on.
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LucyTheApe Inactive Member |
"Rrhain" writes: It is better to keep silent. It's better to tell the truth.
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Hyroglyphx Inactive Member |
Prisoner's dilemma - Wikipedia
There is some risk, regardless. But the "Nash Equilibrium" levels the playing field to cooperation being the safest route. Edited by Nemesis Juggernaut, : No reason given. “Tu ne cede malis sed contra audentior ito"
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lyx2no Member (Idle past 4716 days) Posts: 1277 From: A vast, undifferentiated plane. Joined: |
Hoping I've the good sense not to entwine myself in these situations often enough that the cooperation route becomes the best alternative, but rather as this is a one-off, ratting out the other guy is the best option; it offers no time or five years. let's also hope the other guy does intend to make trouble his vocation and plans for the long term.
Kindly Were Christians ever to speak in non-ambiguous terms and listen with critical ears there would soon be no Christians for lack of agreement as to God plan.
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Modulous Member Posts: 7801 From: Manchester, UK Joined: |
Prisoner's dilemma - Wikipedia There is some risk, regardless. But the "Nash Equilibrium" levels the playing field to cooperation being the safest route. Only if we are using the iterated prisoner's dilemma. In the classic setup as in the OP defection dominates. From that very wiki page:
quote: The wonderful thing about the iterated prisoner's dillemma is its application to the evolution of morality. According to game theorists the best strategies are generally (as per the wiki page) Nice (it will not defect before its opponent does)Retaliating (It must sometimes retaliate.) Forgiving (Though players will retaliate, they will once again fall back to cooperating if the opponent does not continue to play defects. This stops long runs of revenge and counter-revenge, maximizing points.) Non-envious (not striving to score more than the opponent) Instead of Nash equilibria we deal with the related concept of Evolutionarily Stable Strategies. I see this as the best argument against the 'We all share a common sense of right and wrong because of an objective moral standard', since there need be no objective moral standard when we apply game theory: Such systems pretty much make themselves.
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Rrhain Member Posts: 6351 From: San Diego, CA, USA Joined: |
Modulous responds to me:
quote:quote: It has to do with, as another mathematician friend of mine says, "Thinking like a mathematician, not an economist." That is, you can graphically show the strategy to follow by drawing two vertical scales and drawing lines connecting the two. That is, if Red cooperates and Blue betrays, then you draw a line from the -10 of Red's scale to the 0 of Blue's scale. Once you get them all written up, you look at the highest low point. That is, when approaching the intersecting lines from the bottom, at what point do you reach the highest intersection? In this case, since it'd be the -5 line, you'd think that that would be the best solution. After all, the worst you could do is 5 years and you have the possibility of getting none. But, that's thinking like an economist. Instead, come from the other side. The winning solution is to cooperate. Your winnings are six months. An economist will look at this and always betray (yes, they have done studies of this). The mathematician, however, will look at this and cooperate. ...and come out ahead. The mathematicians look at the problem and think to minimize the entire outcome. After all, the other guy is supposedly your friend. When they look at the problem, they are seeking a solution that reduces the entire amount of time spent in jail. The economists, on the other hand, are looking at the problem and seeking to minimize the individual outcome. Forget about the other guy and him supposedly being your friend. When they look at the problem, they are seeking a solution that reduces only their own time spent in jail. Edited by Rrhain, : No reason given. Rrhain Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.
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Minnemooseus Member Posts: 3941 From: Duluth, Minnesota, U.S. (West end of Lake Superior) Joined: Member Rating: 10.0 |
Rrhain writes: An economist will look at this and always betray (yes, they have done studies of this). The mathematician, however, will look at this and cooperate. ...and come out ahead. The mathematicians look at the problem and think to minimize the entire outcome. After all, the other guy is supposedly your friend. When they look at the problem, they are seeking a solution that reduces the entire amount of time spent in jail. The economists, on the other hand, are looking at the problem and seeking to minimize the individual outcome. Forget about the other guy and him supposedly being your friend. When they look at the problem, they are seeking a solution that reduces only their own time spent in jail. Moose, in message 3 writes: I would think that IF each knows each other AND have a very trusting bond, both will remain silent and take the 6 months. Otherwise, they would each betray the other an assure that they do not get the maximum penalty, and possibly will get off entirely. I'm showing signs of being smarter than I think I am (I think). Moose
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Modulous Member Posts: 7801 From: Manchester, UK Joined: |
You seem to be attempting to describe super-rationality. Super-rationality differs from rational thinking as per Game Theory, though I've never come across the mathematician/economist divide you mention.
Super-rationality is hardly such an established phenomenon that you can comfortably declare the Game Theory answer 'incorrect' in such absolute terms. Super-rationality requires that your opponent will necessarily pick the same answer as you do, which means that mixtures of defect and cooperate will never happen. Therefore the choices are Betray/Betray or Cooperate/Cooperate, and so Cooperate dominates. Personally, I think this essentially undercuts the point of the game by assuming that your opponent is super-rational (ie., knowing what your opponents strategy is (and knowing they will stick with it)) is tantamount to communication between players. And of course, a super-rational player versus a Game Theory player will always lose, unless the super-rational player can somehow establish he plays against a Game Theory player. If we say that the super-rational player is unsure about the strategy of his opponent - then things become much less clear-cut with certain judgements required about the probabilities and cooperating with a certain optimum probability.
An economist will look at this and always betray (yes, they have done studies of this). The mathematician, however, will look at this and cooperate. ...and come out ahead. Using your phraseology: The mathematician will cooperate and come out ahead, only if he plays against a mathematician. If he plays an economist, he comes out way behind.
The mathematicians are seeking a solution that reduces the entire amount of time spent in jail. Then they are mathematicians that haven't studied Game Theory. Merrill Flood, Melvin Dresher and Albert W. Tucker, the fathers of the prisoner's dilemma were all mathematicians and concluded 'defect' is the dominant strategy despite mutual cooperation being the optimal solution. This rather paradoxical result is the reason it has been named a dilemma and has been discussed and modified for over half a century. Granted, mathematicians may indeed conclude that the optimal solution is to both cooperate - though I'm sure economists would see that too. Not knowing what strategy your opponent is going to pick ensures that defect remains dominant according to game theory. If we play out a super-rationalist against either a game theoretician 50% of the time and a super-rationalist the other 50%. After 100 trials (with no memory, vengeance etc) The cooperator will get the sucker's payoff 50 times for 500 years in jail. He will get the cooperation reward 50 times for 25 years in jail. He has a total of 525 years in jail or 5.25 years per attempt. The defector under the same conditions will get the defection reward 50 times for 250 years and will get off 50 times for 2.5 years per attempt. Indeed, the cooperator had better hope he meets other cooperators at least 80% of the time because then he gets the suckers payoff 20 times for 200 years and the cooperation reward 80 times for for 40 years in prison and under these circumstances he will get 240 years or 2.4 years in prison per go on average. Of course, with so many cooperators the defectors still do better. They now get off 80 times and only spend time in jail 20 times for 100 years or 1 year in prison on average.
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Rrhain Member Posts: 6351 From: San Diego, CA, USA Joined: |
Modulous responds to me:
quote: No, I'm pointing out that it depends upon what game you're playing. One way to look at it is to attempt to minimize the amount of time spent in jail across all. In that case, the winning answer is to cooperate since mutual betrayal is equivalent to singular betrayal: Ten years. But mutual cooperation results in only one year. Since the only way to achieve the minimum time spent is to cooperate, the winning solution is to go for it. The other way to look at it is to try to minimize the amount of time spent by an individual. In that case, you would betray as the only way to minimize your time is to betray. Which game are you trying to play?
quote: (*blink!*) You did not just say that, did you? Game theory is mathematics. Who else would understand it but mathematicians? The point I am trying to make is that the question of the "winning strategy" has more to do with the type of game you are playing. That's why it's called a "dilemma": It is pitting the rationality of the individual against the rationality of the group. Which game are you playing?
quote: No, that's just it: They don't. Even when shown that the optimal solution is to cooperate, they betray. They think that somehow the rules don't apply to them and they always end up with both getting five years. What game are you trying to play? Rrhain Thank you for your submission to Science. Your paper was reviewed by a jury of seventh graders so that they could look for balance and to allow them to make up their own minds. We are sorry to say that they found your paper "bogus," specifically describing the section on the laboratory work "boring." We regret that we will be unable to publish your work at this time.
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