[25 marks] (Aghion and Tirole’s model of delegation) CEO Alice needs to choose among four projects. She hiresBob to recommend a project to her. The four projects are of three types, A, B, and D. One project is of type A,one project is of type B and two projects are of type D. Both Alice’s and Bob’s payoffs depend on the types of theproject implemented, as summarized in the following table. The payoffs are “utility indices” whose expectation iswhat players try to maximize.Throughout the question, we assume that Alice cannot observe the types of the four projects: the four projects lookidentical to her. The timing is as follows.(1) Bob recommends a project based on his knowledge.Project type Alice’s payoff Bob’s payoffA 10 6B 6 10D -100 -1001(2) Alice chooses among three options: implementing the project recommended by Bob, implementing a randomlychosen project not recommended by Bob, and doing nothing. Doing nothing gives both players zero payoff.(a) [5 marks] First, assume that Bob knows nothing more than Alice. Therefore, he randomly recommends aproject, which is of types A with probability 1/4, B with probability 1/4, and D with probability 1/2. Determinewhat Alice should do in this case.(b) [15 marks] Now assume that Bob knows the types of the four projects. We model the interaction betweenAlice and Bob as a strategic form game. Bob chooses which project to recommend (A, B or D) and Alicechooses among C (accepting the recommendation), R (rejecting the recommendation and choosing randomlybetween the remaining three projects) and N (doing nothing). Write down the payoff matrix of the game andfind all Nash equilibria (in pure strategy). (Hint: first, figure out the probabilities that Alice’s randomly chosenproject is of type A, B and D if she rejects Bob’s recommendation.)(c) [5 marks] Discuss why hiring Bob (whose salary is negligible compared with project payoffs) may help Aliceeven though their interests are not perfectly aligned. (Limited to 50 words.

Consider a firm in which a boss can choose to either centralise decision making (C) or to delegate to an agent (D). If the boss opts for C the payoffs are 15 for herself and 20 for the agent. If the boss chooses D, this is observed by the agent who can then choose to but in low effort (L) or high effort (H). If the boss chooses D and the agent L the payoffs are 10 apiece. If, on the other hand, the boss opts for D and then the agent chooses H the payoffs are 30 to the boss and 15 to the agent. a. Draw the extensive form (or game tree) of this game. Solve for the Nash equilibria and for the subgame perfect equilibrium. Provide intuition for your answer. What relation does you answer have to the theories on delegation studied in class? (5 marks) b. Now consider the outcome of the game if the payoff to the agent in the case of centralisation is 35 (not 20). What is the SPE? With reference to the basic value maximisation principal, what are the implications for the boss and agent in this organisation? (5 marks) c. Consider again the original payoffs (that is the agent’s payoff following centralisation is 20), but allow the agent to move first (choosing either L or H) before this is observed by the boss who then makes their choice of C or D. What is the SPE of the game? Interpret the results in the light of the Aghion and Tirole model studied in class. (5 marks)

The Texas Consolidated Electronics Company is considering an R&D program encompassing eight research projects. In the model for this problem Xi is a 0-1 variable for the selection of project i, where i = 1 to 8. One of the conditions in the model is that the same decision be applied to project 2 and project 5. If project 2 is selected then project 5 is selected. And if project 2 is not selected then project 5 is not selected.  This condition is represented by the following constraint:

Evaluate the statement: According to Kaldor Hicks Criterion, we should only accept a project when at least one individual is better off without making any other individual worse off

A principal can either legally make a decision herself (P-formal authority) or can decide to assign the formal right to make a decision to her subordinate (delegation). In each case the party that has the formal right to decide can make a decision on a new project. If that party is uninformed they will defer the decision to the other party who will decide if they are informed. The principal’s effort level of finding a new project is denoted by E; e denotes the subordinate’s effort level. E and e represent the probability that both the principal and the agent discover a new project. The following table provides the effort levels of both parties under P-formal authority and delegation. P-formal authority Delegation Principal E = 0.8 E = 0.4 Agent e = 0.5 e = 0.8 If the principal’s preferred project is chosen, the principal gets a revenue/benefit of $100. Finally, the probability that the agent’s preferred project is also preferred by the principal is a = 0.8. What is the principal’s expected benefit (not including effort costs) with P-formal authority? Answer with a number only (no words or symbols such as $ signs).

QUESTION 3The table below summarises the potential net benefit for four individuals involved in four distinct projects. Which statement in relation to Pareto conditions is most correct? Project A Project B Project CProject DBob48362412Anna33276845David-88-34-6425Caroline63-25-4226Both project A and project B are examples of potential Pareto improvement. Project C is an example of strict Pareto improvement. Only project A represents an example of potential Pareto improvement.Both project A and project B are an example of strict Pareto improvement.