Problem 1: [20 pts] Consider the following normal form game: For the following parts, let 92 = (1/2,1/2) be a belief that assigns probability 1/2 to both L and R. Let 9'2 = (2/3, 1/3} be a belief that assigns probability 2/3 to L and U3 to B. Part a." [10 pts] Suppose that :r: = U. Is the mixed strategy 01 (1/2,0,1/2} a. but response against 32? Explain why or why not. Part I): [10 pts] Suppose now that 13 = 1. Is the mixed strategy :71 = (1/2,0,1/2} a. best response against Hg? Explain why or why not. Part c: [10 pts] Suppose again that I = {1. Is the mixed strategy 0'1 = (1/2, 0, 1/2} a best response against the belief 6'; = (2/3, 1/3)? Explain why or why not