1. (10pts) For the following game (Player 1 chooses T or B; Player 2 chosses L, C, or R): payoffs L C R T 2, 4 0, 3 1, 2 B 3, 0 1, 1 10, 3 Note: (b) can be solved without solving (a). (a) (5pts) Show that for player 2, some mixed strategy involving only L and R, qL + (1 - q) R, strictly dominates pure strategy C. (You should find some value of q for it to be true.) (b) (5pts) Now, eliminate strategy C. Then find all mixed-strategy and pure strategy equilibria in the simplified game. (Hint: no need to use mixed-strategy best response functions.)