2. There are three firms: firm 1, firm 2 and firm 3. Each firm $i$ chooses the level of production $q_i$. The market price is determined by market demand: $p = 24 - q_1 - q_2 - q_3$. And the marginal cost of production is zero.
(a) Suppose firm 1 moves first, then firm 2 moves and finally firm 3 moves. Each firm can observe the previous firms' production strategies. Find all the subgame perfect equilibria.
(b) Suppose firm 1 moves first, and then firm 2 and 3 move simultaneously. Find all the subgame perfect equilibria.