Modulous responds to me:
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Can you name any mathematicians who pick 'cooperate'?
Well, there's me. And then there's all the professors in my various probability and statistics classes.
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How many of them have studied Game Theory?
All of them. That's why they were the professors of the classes. They were teaching it.
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As I said, I've never seen this economics vs mathematics divide on this issue.
And I have. So now what?
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In your opinion however, "The mathematicians are seeking a solution that reduces the entire amount of time spent in jail." - which would tell me that these particular mathematicians haven't studied game theory...unless they are using super-rationalism as justification.
There's another option, you know....
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No, it's called a dilemma because "The unique equilibrium for this game is a Pareto-suboptimal solution”that is, rational choice leads the two players to both play defectly even though each player's individual reward would be greater if they both played cooperately."
That's not a dilemma. And you do know that Wikipedia isn't really a source, but since you seem to want it, I notice you didn't pay attention to your own article:
Wikipedia's entry on "Pareto efficiency" writes:
Pareto efficiency, or Pareto optimality, is an important concept in economics with broad applications in game theory, engineering and the social sciences.
Hmmm..."important concept in economics"...I wonder why there might be a distinction between the economic interpretation and the mathematical one....
But, let's continue with your own source:
Wikipedia's entry on the "Prisoner's Dilemma" writes:
Rational self-interested decisions result in each prisoner's being worse off than if each chose to lessen the sentence of the accomplice at the cost of staying a little longer in jail himself. Hence a seeming dilemma.
Hmmm...wasn't that what I was saying? That there is the game of self-interest and the game of group-interest, that they are not the same, and players that go for group-interest will do better than those that go for self-interest?
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I mean, if we assume that the object of the game is to go to prison for maximum amount of time, everything changes.
Indeed, which is why the economic interpretation is different from the mathematical one. The economic interpretation is to minimize the individual one. The way it is usually presented in all my classes on the subject, the idea was to reduce the total amount of time spent in jail.
But even so, let's look at the sentence before the one you quoted:
Wikipedia's entry on the "Prisoner's Dilemma" writes:
In this game, as in all game theory, the only concern of each individual player ("prisoner") is maximizing his/her own payoff, without any concern for the other player's payoff.
That's not true. The only concern is not always maximixing his/her own payoff. While it is a common one and most game scenarios are presented as such, sometimes the goal is different.
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If we assume the object of the game is to kill the guards and create a prisoner uprising to overthrow the shackles of oppression, then the optimum solution changes.
(*sigh*)
Let's not play dumb. The only options are to cooperate or defect. The only payouts are various lengths of time.
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Every mathematician agrees that betrayal is the best rational strategy.
(*sigh*)
As an individual strategy, yes. Who said that was the game?
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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.
I have no idea what you are talking about here.
That even when they know that they can optimize for all, they will choose to betray in order to optimize for the individual. This even goes to the iterative game. Even when they know that the winning solution for the iterative game is to play tit-for-tat/forgive/don't get nasty first, they will be likely to betray. It's why we keep running into the tragedy of the commons.
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The optimal solution might well be to BOTH cooperate, but you cannot communicate with the other prisoner.
Who said you were? You both know the outcome. If you're playing the game of getting you both out, then you know what to do.
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Since you cannot cooperate, mathematically speaking your best strategy is to betray.
"Cannot"? Why not?
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What game are you trying to play?
The one where we have to assume that both prisoner's are rational agents.
That's not an answer. That's an assumption of the game. A rational player playing a game of minimizing jail time for all will cooperate.
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Now you seem to be suggesting that it isn't that I was incorrect at all, but that it depends on what game we are playing.
As one who does support for a living, this is always a problem: Unstated assumptions. I was assuming that the game was as it was presented to me. Instead, we're now talking about something else.
When I do a training, I steal something that I saw in
Foxtrot:
A train leaves Station A where the clock reads 10 am, arriving at Station B, 180 miles away, at where the clock reads 2 pm.
Now, the common question at this point is, "What is the average speed of the train?" and the expected answer is "45 mph." But instead, the question I put is:
What do we need to assume in order to determine the average speed of the train?
There's quite a list:
The clocks are working.
The stations are in the same time zone.
The train arrives on the same day.
The track goes directly to the station and doesn't waver.
The track is taking the short way instead of going around the other side of the globe first.
The track is following the curvature of the earth and isn't tunneling through as a chord.
Ignoring relativistic effects of moving bodies in a gravity field.
I was assuming a different game than you were.
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You don't even know what the probabilities are of your opponent picking cooperate.
There aren't any. You assume a rational player. That's the point.
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Can you find any websites that support your position? I can only find ones that don't and what you write intrigues me.
(*blink!*)
You've never heard of "sub-optimization"? OK.
The problem of suboptimization
Optimizing the outcome for a subsystem will in general not optimize the outcome for the system as a whole. This intrinsic difficulty may degenerate into the "tragedy of the commons": the exhaustion of shared resources because of competition between the subsystems.
When you try to optimize the global outcome for a system consisting of distinct subsystems (e.g. maximizing the amount of prey hunted for a pack of wolves, or minimizing the total punishment for the system consisting of the two prisoners in the Prisoners' Dilemma game), you might try to do this by optimizing the result for each of the subsystems separately. This is called "suboptimization". The principle of suboptimization states that suboptimization in general does not lead to global optimization. Indeed, the optimization for each of the wolves separately is to let the others do the hunting, and then come to eat from their captures. Yet if all wolves would act like that, no prey would ever be captured and all wolves would starve. Similarly, the suboptimization for each of the prisoners separately is to betray the other one, but this leads to both of them being punished rather severely, whereas they might have escaped with a mild punishment if they had stayed silent.
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Can you find this economists vs mathematicians study?
If you can wait, I'll ask my colleague as he is the one who presented it to me. He, too, is a mathematician who crossed to the dark side and went into economics.
He got better.
By the way, a good textbook game theory, involving games with multiple choices ("Gladyn and Don inherit a car worth $800. The evils of communism being well known to them, they agree to settle the ownership by means of sealed bids. The high bidder gets the car by paying his brother the amount of the high bid. If the bids are equal”which they may well be, because they agree to bid in hundred-dollar quantities”the ownership is determined by the toss of a coin, there being no exchange of funds. Gladyn has $500 on hand, whereas Don has $800. How should they bid?"...this is a 5x8 game with multiple saddle points):
The Compleat Strategyst: Being a Primer on the Theory of Games of Strategy by J. D. Williams.
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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