Reference no: EM131704558

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<m<n (The m players might simply don't want to think hard, they might be stock traders who always buy the most expensive stock regardless). The remaining n-m players are rational, and they know that they are rational, and know that they know that they are rational, and so on. In addition, these n-m rational players know that m players are irrational (i.e., they always write100), and they know that they know that the m players are irrational, and so on. How will then n - m rational players play the game?