Guess Two-Thirds of the Average
Everyone in a group privately writes down a whole number from 0 to 100. Whoever's number is closest to two-thirds of the average of everyone's guesses wins. There's no hidden information and no trick — just a room full of people trying to outguess each other, who are themselves trying to outguess you outguessing them. What number should you pick?
Reveal the answer
Pure logic drives the answer all the way to 0: if everyone reasons this way infinitely, the only guess nobody can be beaten on is 0. In practice, real players stop after two or three rounds of thinking about what others think, so winning guesses actually cluster in the low-to-mid teens. The game became a classic test of bounded rationality after Alain Ledoux used it as a magazine tiebreaker in 1981, echoing Keynes's older newspaper beauty-contest analogy for markets.
— Alain Ledoux, Jeux et Strategie magazine tiebreaker game — 1981