Answer all parts:

Part a: Consider the following normal form game: D E F A 1,1 1,0 1,0 B 0,1 m,0 0,37 C 0,1 0,m 50,0 Let ((a, b, c), (d, e, f)) be the mixed strategy prole where player 1 chooses A with probability a, B with probability 1), C with probability 0; and player 2 chooses D with probability d, E with probability 6, and F with probability f. For what values of x (a: can be negative or positive) is the strategy prole ((0,1/2,1/2),(0,1/2,1/2)) a mixed strategy Nash equilibrium? Part b: 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