Suppose a manager (player 1) and a worker (player 2) have a contractual relationship with the following technology of interaction. Simultaneously and independently, the two parties each select either low (L) or high (H) effort. A party that selects high effort suffers a disutility. The worker's disutility of high effort (measured in dollars) is 2, whereas the manager's disutility of high effort is 3. The effort choices yield revenue to the manager, as follows: If both choose L, then the revenue is zero. If one party chooses L while the other selects H, then the revenue is 3. Finally, if both parties select H, then the revenue is 7. The worker's payoff is zero minus his disutility of effort (zero if he exerted low effort), and the manager's payoff is her revenue minus her disutility of effort.
(a) Draw the normal-form matrix that represents the underlying game.
(b) If there is no external enforcement, what would be the outcome of this contractual relationship? (
(c) Suppose there is external enforcement of transfers but that there is limited verifiability in that the court can only observe the revenue generated by the parties. Explain how this determines which cells of the matrix the court can distinguish between.
(d) Continuing to assume limited verifiability, what is the best outcome that the parties can achieve and what contract will they write to achieve it? (Assume maximization of joint value.)
(e) Now assume that there is full verifiability. What outcome will be reached and what contract will be written?