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Topic: question about decision theory (Read 1221 times) |
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Benny
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question about decision theory
« on: Feb 4th, 2008, 1:09pm » |
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After contemplating the higher-order reasoning involved in a game of Chess, one might but wonder: Are there mathematical approaches or optimisation procedures that can be employed when interacting with other humans in a situation that "demands" higher-order reasoning? (Chess, Warfare, Hunting...)
The Prisoner's Dilemma and other, similar thought experiments assume predictable, synchronised behaviour. However, if we apply the same 'psychology' (if you like) to a game of Chess, it seems unreasonable to suppose that participants will 'defect' (I can't even see how one might). Instead, at each turn, we must guess at the order of reasoning employed by our opponent - this is tantamount to a figure; 1st, 2nd and so on...
First: How can I attack?
Second: How might my opponent counter-attack?
Third: How might I counter his counter-attack?
...etc...
This, IMHO, realistically describes human thought. All ideas are welcome.
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If we want to understand our world — or how to change it — we must first understand the rational choices that shape it.
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towr
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Re: question about decision theory
« Reply #1 on: Feb 4th, 2008, 1:42pm » |
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on Feb 4th, 2008, 1:09pm, BenVitale wrote:| The Prisoner's Dilemma and other, similar thought experiments assume predictable, synchronised behaviour. |
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Not really; they simply aim to arrive at the most rational strategy; the strategy that will give you the best result regardless of your opponent's strategy (be it rational or not).
And it only needs to be synchronized, in the case of the prisoners dilemma, to the point you can't influence your opponents choice or vice versa; separation is sufficient.
Quote:| However, if we apply the same 'psychology' (if you like) to a game of Chess, it seems unreasonable to suppose that participants will 'defect' (I can't even see how one might). |
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It seems unreasonable to me to suppose the prisoner dilemma aims to say anything about chess. You can't really play chess cooperatively either, it's zero-sum (unlike PD). And conversely you can't take someone's pieces in PD, or promote pieces. And you can't score a goal in either game.
Optimal strategy for chess would involve working out the entire game tree with min-max algorithm.
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Benny
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Re: question about decision theory
« Reply #2 on: Feb 5th, 2008, 2:55pm » |
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Thanks.
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If we want to understand our world — or how to change it — we must first understand the rational choices that shape it.
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