Consider the following variant of the Aghion and Tirole (1997) model. A principal Poppy (P) can choose to either Centralise (C) or Delegate (D). If she delegates, an agent Aiden (A) has the decision-making rights about which project to implement. If Poppy chooses to centralise, she retains decision-making powers about which project to implement.

The issue is that ex ante, neither party is informed about what is a good project and what is not. If neither party is informed, no project is implemented, and each player gets a payoff of 0. With centralization P can exert effort E at costs ()E2, which allows her to become informed with probability E. With centralization, if the principal is informed she knows everything about the potential payoffs and will choose her preferred project, which gives her a payoff of B < 1. However, with probability (1 - E) P remains completely uninformed. The agent's preferred project gives him a payoff of b, but the principal's preferred project is also the agent's preferred project with probability . If the non-preferred project for the agent is implemented his payoff is zero. Finally, with centralization, if the principal is uniformed no project is chosen (as noted above) and the game ends.

Alternatively, rather than centralization, the P can chooses to Delegate the decision to A. In this case, the agent can choose to become informed exerting effort e, at a cost of ()e2. Exerting effort e allows A to become informed with probability e (and he remains uninformed with probability 1- e). If A is informed and has been delegated decision-making rights, he will choose his preferred project and get a payoff of b < 1. In this case, P also gets her preferred project and B with probability . If a non-preferred project is chosen by the agent the principal receives a payoff of zero. Finally, with delegation, if A is uninformed (which occurs with probability 1 - e) no project is implemented, and both parties receive a payoff of zero.

a. What are the efforts that P and A put in under the C and D decision-making structures? Interpret your results.

b. Assume that B= b. When will P opt for Delegation? Explain your answer.