I just read an article on Game Theory and the Traveler's Dillemma (Scientific American, June 2007). In it, they explained how the "rational" choice (as explained by Game Theory) was almost never chosen by actual people, and that the "rational" choice generally fared worse than real people did. The simple answer, is that the so called "rational" choice relies upon foolish assumptions.
The dillemma is this: You and another traveler have to pick a number between 2 and 100. Whoever gives the lower number gets paid that amount +2, and whoever gives the higher number is paid that amount -2. If they both give the same number, they both recieve that amount.
The so called "logic" that is supposed to be rational, is to realize that whatever number they choose, you should go one lower, and whatever number you choose, they should go one lower. Following through the logic of what you think, they think, you think, etc... eventually degenerates to a final answer of 2, because if they choose 2, you can't do better than to choose the same. The flaw is the assumption of how the other person thinks (and thus will act).
My answer is this: you don't know them, so you can't assume how they will think. So, I believe it is best to assume all numbers are equally likely to be chosen by them. Then I just start comparing options.
If I choose 100, I get either 100 (if they choose 100) or I get whatever they chose -2.
If I choose 2, I get either 2 (if they choose 2) or I get 4. So if they choose 2, 3, 4, or 5, my choosing 2 is better than 100. If they choose 6-100, then my choosing 100 is better. Clearly 100 is better.
If I choose 99, then I get 101, if they choose 100, and 99, if they choose 99. Two results better than if I choose 100, and the rest are all the same. So 99 is better than 100.
I continued this for a bit, until I found that 97 was better than 98, equal to 96, and better than 95.
So I conclude that the most rational choice is 97. If you have reason to expect the other person to follow this rational, 96 might be better, but going lower is generally not wise without a very strong reason to believe the other person's choice is going to be low.
