Problem 2. Continue to consider the market described in the previous problem, however make the following change. Suppose the same industry exists for an infinite number of periods, the discount factor for profits is still = 0.9. Firms are considering the following strategy:

* As long as no firm has cheated, play according to the agreement to optimize joint profits and split the proceeds.

* If either firm has cheated in any earlier period, play the static Nash equilibrium in every period from now on.

1) If both firms follow the proposed strategy, what is the present discounted value of each firms profits?

2) If one firm decides it will cheat on the agreement and violate the strategy, what is the highest profit that firm can achieve?

3) Based on your previous answers in this question, is the proposed strategy an equilibrium? Why or why not?

4) What is the lowest discount factor, that the firms could have for the proposed strategy to be an equilibrium?