QUESTION 3 Suppose a,b,ceR and you are given symmetric game below. a, a b, c c, b d, d consider the modified utility amounts in games 2, 3, and 4, where x>0: ax, ax bx, cx b, c* a+x, a+x c+x, b+x b+x, c+x d+x, d+x a, at c", bt cx, bx dx, dx For each of the solutions write down which of the games (2, 3, and 4) are guaranteed to have the same solutions as Game 1: a) Pareto optimal cells b) Nash equilibrium cells C) Mixed strategy Nash equilibrium probabilities d) Prove your answer in c) with respect to Game 2 (show your work on the back of this page) QUESTION 3 Suppose a,b,ceR and you are given symmetric game below. a, a b, c c, b d, d consider the modified utility amounts in games 2, 3, and 4, where x>0: ax, ax bx, cx b, c* a+x, a+x c+x, b+x b+x, c+x d+x, d+x a, at c", bt cx, bx dx, dx For each of the solutions write down which of the games (2, 3, and 4) are guaranteed to have the same solutions as Game 1: a) Pareto optimal cells b) Nash equilibrium cells C) Mixed strategy Nash equilibrium probabilities d) Prove your answer in c) with respect to Game 2 (show your work on the back of this page)