Consider a duopoly model where two firms compete in their prices sequentially. 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.