jmatonak

Suppose you and I are both guests at a hotel. We happen to have two identical... things. Lets assume we have identical pottery that we bought from a street vendor. Our pots get broken, and the hotel manager agrees that the staff is at fault. He agrees to supply each of us with the replacement value of our pots, but (to prevent us from hiking the price) asks us to report the price we paid separately. He knows that the price cannot be less than $2 or higher than $100.

He stipulates that he will pay the lower of the two prices we report. He will give an extra two dollars to the person who reported the lower price, taking that out of the money given to the person who reports the higher price. So, if I say the pots cost $15, and you say the pots cost $10, you get $12 and I get $8. If we both report the same price, we each get that amount of money. (He says he's doing it this way to keep us honest.)

Under the usual assumptions of game theory, where you are a "rational actor" seeking to maximize your guaranteed return, you reason thusly:

( This is the bit that was in that Russell Crowe movie. )

Almost without exception, players (even game theorists) say "screw the rational answer" and just pick a high number. And they get better payoffs.