Guess Two-Thirds of the Average

Start simple. If people picked at random, the average would be about 50, so the winning number would be about 33. But if everyone thinks that, everyone picks 33, and the winning number becomes 22. Each extra step of reasoning pushes the answer lower. If everyone reasoned all the way, they would all pick 0. Game theorists call 0 the equilibrium: once you know what the others chose, nobody would want to change their own number.

Real people don't play like that. When Rosemarie Nagel ran this game with groups of 15 to 18 people playing for a cash prize, the first-round average was about 37 and the middle guess was 33. Many people picked numbers close to 33 or 22: they had thought one or two steps ahead, then stopped. Over four rounds, the guesses fell as players learned how the others played. The best guess is never the "logical" 0. It is a good prediction of what the people around you will do.

The economist John Maynard Keynes saw the same logic in financial markets. In 1936 he compared investing to a newspaper contest in which readers pick, from a hundred photographs, the faces they think the other readers will pick. To win, you don't choose the faces you like best, but the ones you expect others to choose. When people buy because they expect others to buy, their expectations can make themselves come true.