2. Repeated Stackelberg: Suppose the demand and marginal costs remain the same as in 2. however now the firms engage in Stackelberg competition, i.e. firm 1 chooses q, first and then firm 2 observing q, chooses 42- (a) Find the Nash Equilibrium quantity of the stage game (not repeated, i.e. the one interaction Stackelberg from week 6). Assume that the firms repeat this sequential quantity competition infinitely, and have common discount factor 6. This means every stage is itself composed of two periods- firm 1 chooses q then firm 2 chooses 92, profits realize after these two sub-periods, the firms observe each other's quantity decisions and then the game repeats. We will construct a grim trigger strategy to sustain the monopoly quan- tity. Let the monopoly quantity be Q and the stackelberg quantities from the previous question be (of, 95). You can replace these by the actual numbers, I just did not want to give away the answers in this question. For firm 1, if the history is (q;. Q" -q;) then play q, = of. Otherwise play q = qi. For firm 2, if the history is (q;, Q" - q;), and firm 1 has played q; in the current round play ga = Q" - qi. Otherwise choose or = 12 - 4, i.e. firm 2 myopically best responds