16. relative performance evaluation Ralph is at it again. Output from the production process owned by Ralph can be x1 or x2. The manager’s input can be L or H. Ralph is risk neutral. The manager is the usual normalized, constant risk aversion type. His risk aversion measure is ρ = .0001; and cH = 4, 000 along with cL = M = 0. The probabilities are given by π(x1|H) =

0.1 and π(x1|L) = 1. Ralph wants supply of input H. The only observable for contracting purposes is the manager’s output. Pretty standard stuff so far.

(a) Determine an optimal pay-for-performance arrangement.

(b) Suppose Ralph owns two such production processes and employs an identical manager on each. Further suppose the two environments are perfectly correlated. So if both managers supply input H, their outputs will always agree (both x1 or both x2). Suppose Ralph offers to pay each 4,000 if their outputs agree and -10,000 otherwise. Verify that if one manager supplies input H the best the other can do is supply input H.

(c) What happens in the above arrangement if one manager supplies input L? Is the other’s best response also to supply input L? How do you think the managers will play the game?

(d) Amend Ralph’s scheme so that, in the game played between the two managers, both supplying input H is a unique equilibrium.
Give an intuitive explanation for why your modification leads to a unique equilibrium. What difficulty is associated with your scheme?