Consider the following "beauty contest" game. There are n>1 players. Simultaneously, each player submits a number between 0 and 100. Payoff: the player(s) whose number is closest to the two thirds of the average x receives a positive prize (the prize is larger if the number is closer to the two thirds of the average), everyone else gets 0. Assume m out of these n players are irrational in the way that they always write 100; where 0