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)

Consider a firm in which a boss and a worker each simultaneously get to choose their actions. The boss can choose between centralizing (C) or delegating (D). The worker can put in low effort (L) or high effort (H). The payoffs are 2 to the boss and 2 to the worker if the choices are C and L. If the boss chooses D and the worker L the payoffs are (1,6) to the boss and worker, respectively. If the actions chosen are C and H the payoff are (6, 1). Finally, if the actions are D and H, the payoffs are 4 apiece. a. If the game is played once, what is the Nash equilibrium. Explain your answer. Could this represent an outcome in a real firm? b. What if the worker and boss meet twice, in which in the first period both make their choice of action simultaneously. Following this, the outcome (and payoffs) is revealed and the game proceeds to the next and final period. In the second period, again the parties simultaneously choose their actions, the payoffs are revealed and the game ends. What outcome do we see in both periods in the subgame perfect equilibria and why? c. Now assume that instead of meeting once or twice, the two players play the simultaneous-choice stage game an infinite number of times. In each period, the two players simultaneously make their choices, the outcome in that period is revealed to all and the players proceed to the next period. Each party discounts future periods by a discount factor δ, where 0 ≤ δ ≤ 1.

[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.

Maria, a supervisor at a petrochemical plant, asks the plant superintendent to hire an additional worker whenever overtime hours for the previous month increase by more than 15 percent over the headcount. What type of decision is this?Multiple Choiceintuitivegroupthinksatisficingboundedprogrammed

Consider this following sequential game played by two investors. Cat chooses either to go long (L) of short (S). Cat’s choice is observed by rival Cutter. Cutter then can choose to either play Hard (H) or Diverse (D). The payoffs are as follows. Following (L, H) the payoffs are (300, 500) to Cat and Cutter, respectively. If the actions are L then D, the payoffs are (0, 0). If the actions are S and then H, the payoffs are (0, 0). Finally, if the actions are (S, D) the payoffs are (300, 500). In the credible (subgame perfect) equilibrium we observe:Group of answer choicesS then DL then HS then HS then LS then D, or L then H.

Consider a game in which Myer and DJs simultaneously choose whether to advertise (ADV) or not advertise (NOT). If both firms opt to ADV, the payoffs are 10 to Myer and 7 to DJs. If both firms choose NOT, the payoffs are (5,8) where the first payoff is Myer’s and the second DJs’. If Myer plays NOT and DJs ADV, the payoffs are (20, 6). Finally, if Myer plays ADV and DJs Not, the payoffs are (15, 12), respectively. Which statement is (most) true?Group of answer choicesDJs has a dominant strategy.Myer does not have a dominant strategy.Myer’s best response to a strategy of ADV by DJs is to play NOT.The Nash equilibrium is (ADV, NOT), for Myer and DJs respectively.All of the above statements are true.