Game theory

Question 1. Firms 1 and 2 offer an identical product on the market such that the demand is given by p = 2 -Q (Q is total quantity) Firm I's marginal cost is of = 0 with probability 1 and observed by both firms. On the other hand, firm 2's marginal cost o, is only observed by firm 2 and unknown to firm 1. Firm 1 believes that 0 with probability + (low-cost type) - with probability + (high-cost type) The game is played over two periods. In the first period, firm 1 chooses quantity q1 e (0, co), which is publicly revealed at the end of the period. In the second period, after q, is observed, firm 2 chooses its quantity 92. The final payoff functions are given as follows. a(q, q) = (2-q -92 - c)q vi = 1,2 (a) Suppose that firm 1 chooses q in the first period. For any q, 2 0, find the best response of each type of firm 2 in the second period. (b) Find the subgame perfect equilibrium