FRIDAY'S KILLER QUESTION: Everyone in a group pays 1 to enter the following competition....
On Friday afternoons we are posting cryptic questions from 7city Learning. Add your answers in the comments box at the bottom of the page. Adulation will be extended to the person who provides the correct answer first. We'll add the official answer to the bottom of this article on Monday afternoon.
Everyone in a group pays 1 to enter the following competition. Each person has to write down secretly on a piece of paper a number from zero to 100 inclusive. Calculate the average of all of these numbers and then take two thirds. The winner, who gets all of the entrance fee, is the person who gets closest to this final number. The players know the rule for determining the winner, and they are not allowed to communicate with each other. What number should you submit?
Answer
This is a famous economics experiment, which examines people's rationality among other things.
If everyone submits the number 50, say, then the winning number would be 33. Perhaps one should submit 33. But if everyone does that the winning number will be 22.
Ok, so submit that number. But if everyone does that... You can see where this leads. The stable point is clearly zero because if everyone submit zero then two thirds of that is still zero, and so zero is the winning number. The winnings get divided among everyone and there was no point in entering in the first place.
In discussions about this problem, people tend to carry through the above argument and either quickly conclude that zero is 'correct' or they stop the inductive process after a couple of iterations and submit something around 20. It may be that the longer people have to think about this, the lower the number they submit.
This is a nice problem because it does divide people into the purely rational, game-theoretic types, who pick zero, and never win, and the more relaxed types, who pick just pick a number after a tiny bit of thought and do stand a chance of winning.
