Week 6 additional questions
1. Consider a delegation game between Paul (the principal) and Ainslie (the agent). There are an infinite number of periods and each party discounts future payoffs by a per‐period discount factor of δ.
In each period Paul can decide whether or not to delegate the decision‐making rights to Ainslie or to centralize (keep the decision‐making authority for himself). The convention at the workplace is that if Paul delegates to Ainslie, Ainslie generates 12 units of surplus by her efforts, then allocates half to each of the parties (they get surplus of 6 each). If Ainslie breaks the convention (or has broken the convention in any previous period) Paul keeps the decision‐making rights for himself. With centralization the per‐ period payoff is 5 to Paul and 4 to Ainslie.
What discount factor is required in order for Ainslie to keep the convention? Why would Paul ever want to delegate?
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What if the payoff to Ainslie after breaking the convention is 0 – what discount factor is required to sustain the convention as a subgame perfect equilibrium? Compare your answer to your previous answer and interpret.
2. Consider a game ‘inspired’ by Aghion and Tirole (1997). A Principal P and an Agent A can simultaneously either put in High (H) or Low (L) effort into discovering a project to implement. The payoffs are as follows. If both parties put in H the payoffs are 23 to the A and 24 to P. If both parties put in L then the payoffs are 12 and 15 to the A and P, respectively. If the A puts in L and P chooses H the payoffs are 25 each. Finally, if A opts for H and P for L the payoffs are 20 for A and 30 for P.
Focusing on pure strategies, what are the Nash equilibria of the game? Interpret in the light of Aghion and Tirole (1997).
Now consider that the Principal can choose the timing of the game: explicitly, the P can choose either H or L, this is then observed by the Agent who can then choose either H or L based on the P’s choice of effort level.
What is the SPE? Interpret in the light of Aghion and Tirole (1997).
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