3. 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 xbe 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

(a) Prove that xi(0,100) is a strictly dominated strategy for each of the m players.(10 pts)

(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 nm players. (challenging question, 5 pts)

(c) Compute the rationalizable strategies whenm= 5 andn= 100? (5 pts)