4. There are three firms i = 0, 1, 2. The game is played over two periods. In the first period, firm 0 chooses quantity go 2 0. In the second period, after they observe go, firms i = 1 and 2 choose their quantities qi 2 0 simultaneously. The payoff of each firm i = 0, 1, 2 is given as follows uo = (1 - Q)qo, u1 = (1 - Q)q1, and u2 = (1 -Q)q2 where Q = qo + q1 + 92 stands for the total quantity. (a) Suppose that firm 0 chooses qo = 1/2 in the first period. Find the Nash equilibrium in the ensuing subgame in the second period. (b) Find the subgame-perfect equilibrium (of the whole extensive-form game). Now, change the timing as follows: two firms i = 1 and 2 choose q1 and q2 simultaneously in the first period, and then, firm 0 chooses go in the second period after it observes q1 + 92. (c) Find the subgame perfect equilibrium under this new timing rule