Problem 1: [20 pts] Part a: /10 pts/ Consider the following normal form game: D E F A 1. 1 10 1,0 B 0, 1 r, 0 0, 1 0. T Let ((a, b, c), (d, e, f)) be the mixed strategy profile where player 1 chooses A with probability a, B with probability b, C with probability c; and player 2 chooses D with probability d, E with probability e, and F with probability f. For what values of z (I can be negative or positive) is the strategy profile ((0, 1/2, 1/2). (0, 1/2, 1/2)) a mixed strategy Nash equilibrium? Part b: [10 pts/ Suppose that both a and a' are distinct pure strategy Nash equilibria of the same normal form game. Is it possible for a to Pareto dominate a"? If yes, provide a concrete example. Otherwise, explain why not. Problem 2: [20 pts] Consider the following normal form game. L M R. A 1,1 3.0 0,1 B 2,0 0.1 4,0 0,0 2.0 1, 1 Part a: (5 pts/ Find all of the pure strategy Nash equilibria of the game. Part b: 15 pts/ Are there any mixed stra