(b) (10 points) Consider the following Simultaneous game, where there are three strategies for both players 1 and 2. Player 2 L C R Player 1 T (12,4) (6,0) (-2,9) M (2,4) (2,14) (12,0) B (6,10) (0,14) (4,4) i. (3 points) Using best responses, is there any pure strategy Nash Equilibria um/Equilibria (NE)? If yes, write it/them out. If no, what does this imply? ii. (4 points) This game can actually be reduced to a 2 game so that mixed strategy NE can be solved easier (if there is any). Use iterated elimination of strictly dominated actions (IESDA) to eliminate actions for player 1 and 2. Write out which action is dominated and HOW it is dominated (if you use a mixed strategy to eliminate another action, you need to specify the set of possible mixes or a particular mix). What is the rationalizable strategy set? iii. (3 points) Using the reduced game to solve for all Nash Equilibrium/Equilib ria of the game. Circle your answer. 9/12 (c) (4 points; this is a previous final exam question) Consider the following three- player game, where each player has three strategies. Find all the pure strategy Nash Equilibria. Show your work (at least on the table below). P3 chooses A P3 chooses a P2 P2 C R PI T (3,0,1) (2,4,2) (1,0.0) M (2,1,3) (4,3,0) (0,2,1) PI T (2,1,0) (3,4,0) (1,2,1) M (1,2,1) (2,3,3) (4,2,2) B (1,0,1) (0.2,2) (5,4,3) B (0,0,0) (4,6,3) (3.4,3)