A manager (M) and employee (E) interact as follows. The manager can choose whether to offer a written contract or simply shake hands with the employee. If the manager offers a written contract, the parties bargain over a wage and a bonus. Then the employee decides whether to work or shirk. Under the written contract, the employee is paid the contractual wage p for sure, and he is also paid the contractual bonus q if he worked. If the parties do not have a written contract, then after the work/shirk decision, they negotiate over the amount that the manager will pay the employee. The extensive form of this game is shown in the illustration that follows. The contractual variables p, q, and r may be any real numbers.
(a) Find a negotiation equilibrium in the subgame that starts at node 1.
(b) Find a negotiation equilibrium in the subgame that starts at node 2.
(c) Consider any negotiation equilibrium of the entire game. What are the equilibrium payoffs?