3. Consider the following delegation versus centralisation model of decision making. loosely based on some of the discussion in class. A principal has to implement a decision that has to be a number between CI and 1; that is_. a decision d needs to be implemented where U 3' d E l . The di'rculty for the principal is that she does not laiow 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 ot' the economy. In other words. it' the economy is in state s (where U E 3 E l) the principal would like to implement a decision a? = 3 as the principal's utility Up [or loss from the maximum possible prot) is given by Up = |3 a" . With such a utility function, maximising utility really means making the loss as small as possible. For simplicity, the two possible levels ot's are 0.4 and ELI. and each occurs with probability [1.5. 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 Us. that is increasing the further from [3.4 the decision aIT that is actually implement. specically. L73 2 |D.4 d | . Similarly. Manager 13 always wants a decision of 0.? to be implement. and incurs a disutility Us that is (linearly) increasing in the distance between 0.? and the actually decision that is implemented - that is [55 = |C|.'r' (fl . Each manager is completely informed, so that each of them knows exactly what the state of the economy a is. [a] The principal can opt to centralise the decision but before making her decision given she does not know what the state of the economy is she asks for recommendations from her two division managers. Centralisation means that the principal commits to implement a decision that is the average of the two recommendations she received from her managers. The recommendations are sent simultaneously and cannot be less than D or greater than 1. Assume that the state of the economy 3 = 0.7. 1What is the report (or recommendation) that Manager A will send if Manager B always truthfully reports 3'? (b) The principal is going to centralise the decision and will ask for a recommendation from both managers. as in the previous question. Now= however= assume that both managers strategically make their recommendations. What are the recommendations rs. and rs made by the Managers A and B. respectively. in a Nash equilibrium? [c] What is the principal's expected utility (or loss] under centralised decision making [as in part b]? {d} 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