From the series "Interesting Mindgames"
February 27, 2007This is a nice game to play in a class in order to try to put students' brain into first gear. Ask everyone to write down on a paper a number between 0 and 100, but mention that they must try to write a number that is as close as possible to 80% of the average of the numbers chosen by the group.
This is likely to fall into a normal curve, skewed towards smaller numbers. If one was playing alone and should guess the average of random numbers, one would guess 40 (considering a minimum knowledge of probabilities). But 80% of 40 is 32 and another student could reason that the first student would choose 40 and, thus, he should write 32. The first student could then reason that the second student would reason like that and choose 80% of 32: 25.6. And so on.
If everyone would reason like this, they all would reach the conclusion that they should choose zero, because everyone would choose zero. This is the Nash equilibrium of the game. However, no group of student that have never played the game would have a majority (or even more than a few) choosing zero. When trying to anticipate other's choices, it seems humans consider other human's behavior to be completely random.
The interesting thing is that if someone does choose zero, he would probably lose the game, despite being "right". He is right from a game-theoretical point of view but plain wrong from a psychology point of view.