Consider a duopoly model where two firms compete in their prices sequentially.(Be careful!) Denote firm 1's price by p1 and firm 2's price by p2. Every firm has a constant marginal cost c > 0 but no fixed cost. Demand functions faced by the two firms are, respectively, q1 = a - p1 + p2 and q2 = a - p2 +p1, where a>0
(a) Find the subgame perfect equilibrium outcome. What are firms' strategies in this subgame perfect equilibrium?
(b) Construct a Nash equilibrium where the two firms set the same price, provide firms' strategies to support this Nash equilibrium, and show that this Nash equilibrium is not subgame perfect.(really need to know part b)