Game Theory

I was over at SomethingAwful.com looking through the the forums (the "goons" there often post some funny/interesting stuff) when I ran across an interesting problem someone posted there involving game theory. If you don't want to you don't want to click the above the link, here is a copy of the problem:

A priestess at Delphi has a record of .99 accuracy in her predictions of human behavior. On an altar before you are two boxes: an opaque one whose contents you cannot determine and a transparent one obviously containing a silver coin, which you judge to have the market value of $1000. She gives you two choices: (1) take only the opaque box or (2) take both boxes. As she correctly tells you, she has or has not previously placed inside the opaque box a large gold coin worth 1000 times the silver one, depending upon whether she expects you, as a rational agent, to take only the opaque box or both boxes. Should you take only the opaque box or both boxes, knowing that 99 out of 100 agents who took both found the opaque box empty? Or should you forego the silver coin and take only the opaque box, knowing that some- although only 1 out of 100- came up with nothing? Why?

The problem is more complex than it looks on the surface, and that becomes apparent if you read through the thread on that discussion. It is easy to say "take both boxes" (a guarenteed somehting is better than a chance at nothing) but then there are a few goons in the thread that show mathematically how it is better to take only the opaque box. Very interesting stuff.

Another game theory problem I remember is called the Prisoner's Dilemma. Basically, you and an adversary are competing for a prize. You have to make one of two choices: either cooperate with your adversary, or betray them. If you both choose to cooperate, you get to split the prize evenly, but if you choose to betray while your opponent chooses to cooperate, you get the whole thing (it works the other way as well). If you both betray each other, you get nothing. So what is your best option?

There was a game show based on this problem at one time called Friend or Foe. It wasn't a very good show, but I thought the premise they used for it was cool. I haven't studied much on game theory (will have to add it to my to-do list), but I dig what I have seen.

Addendum: It occurs to me now, though (after reading further), that if you can mathematically show that it is always better to take only the opaque box, wouldn't the "rational agent" always go for it? Therefore, wouldn't the oracle choose not to put the gold coin in that box 99% of the time? Therefore, the rational agent would be best off going for both boxes. But knowing that changes the way the rational agent should behave in the first place, and you end up right back at square one.

Apparently, this is a variation on Newcomb's Paradox, which is explained very nicely by Wikipedia (Wikipedia rocks!). Go ahead and read it.

I also just realized that certain readers (you know who you are) may find that I am sticking my foot in my mouth big time by posting this, or at least being inconsistent. I don't know how to reconcile that other than to say that if my college philosophy course had gone into game theory, I might have been able to take it more seriously.