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        riddles >> hard >> question about decision theory
        
(Message started by: BenVitale on Feb 4^th, 2008, 1:09pm)

Title: question about decision theory
Post by BenVitale on Feb 4^th, 2008, 1:09pm

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.

Title: Re: question about decision theory
Post by towr on Feb 4^th, 2008, 1:42pm

on 02/04/08 at 13:09:56, BenVitale wrote:

The Prisoner's Dilemma and other, similar thought experiments assume predictable, synchronised behaviour.

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).

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.

Title: Re: question about decision theory
Post by BenVitale on Feb 5^th, 2008, 2:55pm

Thanks.