please solve this problem

Problem 2 Below, we consider two variants of the beauty contest game described in class. In both games, each player i submits a real number a, E [0, 100], and we let a denote the average guess. 1. Suppose the game has payoff function given by 100 : |x - x| s |x; - x| for every player j u(Ti, 2-i) = : otherwise. Can this game be solved by Iterated Deletion of Strictly Dominated Strategies? What about the Iterated Deletion of Weakly Dominated Strategies? 2. Now suppose that there are 4 players, and player 4 ("the contrarian" ) has payoffs given by us(I) = (14 - x) (i.e. they want to be as far away from the mean). The other 3 players have the payoffs given by 200 - (1; - 22 ) 2. (a) Is strategy r* = 25 strictly dominated by a pure strategy for player 4? (b) Prove that each r4 E (0, 100) is strictly dominated by a mixed strategy for player 4. Hint: Player 4 randomizes over 0 and 100. (c) Compute the set of rationalizable strategies for each player. Show your work