1. Suppose a manager and a worker interact as follows. The manager decides whether to hire or not hire the worker. If the manager does not hire the worker, then the game ends. When hired, the worker chooses to exert either high effort or low effort. On observing the worker's effort, the manager chooses to retain or fire the worker. In this game, does "not hire" describe a strategy for the manager? Explain.
2. Consider a setting in which player 1 moves first by choosing among three actions: a, b, and c. After observing the choice of player 1, player 2 chooses among two actions: x and y. Consider the following three variants as to what player 3 can do and what she knows when she moves:

(a) If player 1 chose a, then player 3 selects among two actions: high and low. Player 3 knows player 2's choice when she moves. Write down the extensive form of this setting, as well as each player's set of strategies. (You can ignore payoffs.)

(b) If player 1 chose a, then player 3 selects among two actions: high and low. Player 3 does not know player 2's choice when she moves. Write down the extensive form of this setting, as well as each player's set of strategies. (You can ignore payoffs.)

(c) If player 1 chose either a or b, then player 3 selects among two actions: high and low. Player 3 observes the choice of player 2, but not that of player 1. Write down the extensive form of this setting, as well as each player's set of strategies. (You can ignore payoffs.)

1. A player displays imperfect recall if at some point in the game he does not know things that he previously knew. In this course will focus exclusively on the case of perfect recall, so a player who knows something at one point in the game will know it at any later point in the game. Explain why the game tree in below violates the assumption of perfect recall.