The question is about microecomics and game theory

4. (20) Consider a duopoly model with product differentiation. Two firms compete in their prices sequentially; firm 1 chooses its price first then firm 2 chooses its price second. Denote firm 1's price by p, and firm 2's price by p2. Each firm has a constant marginal cost c > 0 and no fixed cost. Demand functions faced by the two firms are, respectively, q1 = a - Pi +2 and q2 = a - P2 + p1, where a > c. (a) (14) Find the subgame perfect equilibrium outcome. State firms' equilibrium strategies. (b) (6) Construct a Nash equilibrium where the two firms charge the same price, provide firms' strategies to support this Nash equilibrium, and show that this Nash equilibrium is not a subgame perfect equilibrium