August 9th, 2003

beartato phd

(no subject)

Had a dream that I was lying in bed, and then realized it was a dream. In the dream I had some sort of device which allowed me to "pop out" of dreams. So I used it, and woke up, but found that this device was still there. So, with some trepdation, since I felt very confident that I was in the real world now, I used it again, thinking I was popping out of the universe itself to see what was outside it. Then I, uh, actually woke up. At least insofar as I didn't find any wakey-up device next to my bed this time, and I don't think I'm imaginative enough to dream up all of the contents of the internet.
beartato phd

(no subject)

I'd like to retell a little game-theoretical "paradox" from gustavolacerda, with the numbers changed to make it even more ridiculous:

There is a machine with two buttons. Inside the machine is one million one dollar bills. You and another person take turns pushing buttons. If button A is pushed, the machine spits out $1 (if it still has any left) for the pusher. If button B is pressed, the machine spits out $2 (if it still has that much left), and promptly breaks, allowing no more button-pushing for anyone. All the money inside, of course goes up in smoke, because anyone who has watched any science fiction at all knows that machines emit smoke and sparks and fire whenever anything goes wrong. "She canna spit out enna more than a dollar atta time, cap'n!" or something like that.

The weird thing is that a "rational agent", who seeks to maximize their own gain, and assumes that the other participant is rational also, will push the $2-and-explode button on their very first turn, committing $999,998 to the flames. This is true by a simple induction argument: suppose the machine has just $2 left and it is your turn. Of course you will then push the $2 button. If it has $3, then you reason that if you only take $1, your adversary will take the other $2, so you might as well take $2 now. In general, if the machine has $n, and the inductive hypothesis that a rational agent will push the $2 button on any amount less than $n remaining in the machine, then the "rational" choice is to hit the $2 button, because you know your adversary, being a rational agent, will break the machine on their turn if they get one, so you might as well get $2 instead of $1 on your last turn.

I really like this example because it doesn't require the simultaneity of the prisoner's dilemma to produce what seems like extremely bad behavior which is still rational in the economic sense.

GENERAL DISCLAIMER: I don't mean to say that I think that "rational" in the above sense is actually "good reasoning" necessarily, which is, I think, exactly what the example illustrates. Then again, IANAgame-theorist.
beartato phd

(no subject)

Don't let word get around, or I'll never be able to show my face to my PL friends again, but I wasted a few hours playing with perl. My excuse is that I already had a bitmap editor hacked up from a different project from many years ago, so it was easy to adapt.

The result is that now this makes this.