11. This is an extension of the previous exercise. Consider the following stage game between a manager (also called the "Principal") and a work- er (the "Agent"). Let the manager be player I and the worker be player 2. Simultancously, the manager chooses a bonus payment pe [0, ) and the worker chooses an effort level a E [0. co). The stage-game payoffs are u,(p, a) = 4a - p and utz(p. a) = p - a-. (a) Determine the efficient effort level for the worker. (b) Find the Nash equilibrium of the stage game. (c) Suppose the stage game is to be played twice (a two-period repeated game) and there is no discounting. Find all of the subgame perfect equilibria. (d) Suppose the stage game is to be played infinitely many times in succes- sion (an infinitely repeated game) and assume that the players share the discount factor 8