The car that Erin bought from Sean isnt in great shape and will require annual maintenance. The local Audi dealership conducts the sort of routine maintenance that Erins car needs for a fixed price of $50. As it happens, Sean works part time as an auto mechanic and offers to fix Erins car. However, Sean doesnt know how long it will take him to work on Erins car, and so the only promise he can make to Erin is that hell match or beat the dealerships price. Sean makes an offer to fix Erins car for price p thats between $0 and $50. Simultaneously and without observing the price p, Erin chooses either to accept or reject. If Erin accepts, her payoff is 50 p and Seans payoff is p. If Erin rejects, both of their payoffs are 0.

Question 1:

Consider the situation described at the top of this page. Suppose that Erin enrolls in a local masters program with a two year duration. She intends to keep the car for the duration of her program and then sell it. Identify the subgame perfect Nash Equilibria of the twice repeated stage game with no discounting.

Question 2:

Consider again the situation described at the top of this page. Suppose that Erin enrolls in a local doctoral program with an indefinite duration. Identify conditions on the discount factor under which Sean works on the car every year for $25 as the outcome of a Subgame Perfect Nash Equilibrium in the infinitely repeated stage game with common discount factor . Tip: use grim trigger strategies.