Be sure to write your name and student number on the test. 1. Consider the following coordination game. Player 2 L R " (1,3) (2,3 + () Player 1 B (0,7) (0,5) (a) Suppose e = 1 and find all Nash equilibria. (b) Suppose e = 0 and find all strictly dominant strategies of player 1. (c) Suppose e = 0. Find all pure-strategy Nash equilibria. (d) Continue to suppose e = 0. Find all mixed-strategy Nash equilibria. 2. Consider the following extensive-form game. Note that there are three players and each player has two available actions. Also, note that two nodes of player 3 are in the same information set. Players payoffs are arranged: (payoff to 1, payoff to 2, payoff to 3). a (1, 0, 1) N C d 3 3 (0, 1, 2) (1, -2, 3) (3, 4, 3) (2, -1, 4) (a) Identify all subgames. (b) Show that the following is a subgame perfect equilibrium: Player 1 chooses b, player 2 chooses d, and player 3 chooses f. (c) Is there any other subgame perfect equilibrium? 2