Question -
Consider the following delegation versus centralisation model of decision making, loosely based on some of the discussion in class.
A principal wishes to implement a decision that has to be a number between 0 and 1; that is, a decision d needs to be implemented where 0 ≤ d ≤ 1. The difficulty for the principal is that she does not know what decision is appropriate given the current state of the economy, but she would like to implement a decision that exactly equals what is required given the state of the economy. In other words, if the economy is in state s (where 0 ≤ s ≤ 1) the principal would like to implement a decision d = s as the principal's utility UP (or loss from the maximum possible profit) is given by UP = -|s-d|. With such a utility function, maximising utility really means making the loss as small as possible. For simplicity, the two possible levels of s are 0.4 and 0.7, and each occurs with probability 0.5.
There are two division managers A and B who each have their own biases. Manager A always wants a decision of 0.4 to be implemented, and incurs a disutility UA that is increasing the further from 0.4 the decision d that is actually implement, specifically, UA = -|0.4 - d|. Similarly, Manager B always wants a decision of 0.7 to be implement, and incurs a disutility UB that is (linearly) increasing in the distance between 0.7 and the actually decision that is implemented - that is UB = -|0.7 - d|. Each manager is completely informed, so that each of them knows exactly what the state of the economy s is.
Can you design a contract for both of the managers that can help the principal implement their preferred option? Why might this contract be problematic in the real world?