A manager (M) and a worker (W) interact as follows: First, the players make a joint decision, in which they select a production technology x, a bonus payment b, and a salary t. The variable x can be any number that the players jointly choose. The bonus is an amount paid only if the worker exerts high effort on the job, whereas the salary is paid regardless of the worker's effort.
The default decision is "no employment," which yields a payoff of 0 to both players. If the players make an agreement on x, b, and t, then the worker chooses between low effort (L) and high effort (H). If the worker selects L, then the manager gets -4 - t and the worker gets t. In contrast, if the worker selects H, then the manager gets 8x - b - t and the worker gets b + t - x2 . The interpretation of these payoffs is that 8x is the firm's revenue and x 2 is the worker's cost of high effort, given production technology x.
(a) Represent this game as an extensive form with joint decisions (draw the game tree). Your tree should show and properly label the joint-decision node, as well as the worker's individual decision node. Clearly represent the default outcome and payoff for the joint-decision node.
(b) Given x, b, and t, under what conditions does the worker have the incentive to choose H?
(c) Determine the negotiation equilibrium of this game, under the assumption that the players have equal bargaining weights. Start by calculating the maximized joint value of the relationship (call it v*), the surplus, and the players' equilibrium payoffs. What are the equilibrium values of x, b, and t?
(d) In this setting, is it appropriate to say that the worker's effort is verifiable or unverifiable? Why?