Consider the following version of the beauty contest game. There are n > 2 players. Each player i submits a real number xi ? [0,100]. Let x‾ be the mean of the numbers submitted. Suppose among these n players, there are m players whose payoffs are given by (xi -x‾)2, where 0 < m < n/2. The remaining n - m players have the payoffs given by 200 - (xi -2x‾/3)2. Assume that it is common knowledge in this game that every player is maximizing his/her own payoff.
(a) Prove that xi ? (0, 100) is a strictly dominated strategy for each of the m players.
(b) Compute the set of rationalizable strategies that survive iterated elimination of strictly dominated strategies. You need to figure out the rationalizable strategies of the first m players, and the rationalizable strategies for the remaining n - m
players.
(c) Compute the rationalizable strategies when m = 5 and n = 100?