6. There are n firms: 1, 2, ..., n. Each firm has zero marginal cost. In the given order firms choose their production level, knowing what the previous firms have chosen. That is, Firm 1 chooses q1 2 0 first; Firm 2 observes q, and chooses q2 > 0; Firm 3 observes q, and q, and chooses q3 2 0, and so on. They sell their good at market price P = 1 - (91+ . .. + 9n). Each firm i gets the payoff of qiP. Compute a Nash equilibrium of this game using backward induction for the following two cases: (a) n = 3. (b) for an arbitrary n