Please answer all parts:
Consider a market where the inverse demand is P = 1200 − Q. Firm 1 and firm 2 compete by setting their supply quantities.
(a) Both firms have a unit-cost equal to 300. Assume we can analyze the interaction between firm 1 and 2 as a simultaneous-move game (Cournot model). Find the quantities supplied by each firm in the Nash equilibrium.
(b) Both firms have a unit-cost equal to 300. Firm 1 is a leader in this industry. Assume we can analyze the interaction between firm 1 and 2 as an extensive game where firm 1 moves first and firm 2 moves second (Stackelberg model). Find the quantities supplied by each firm in the subgame perfect Nash equilibrium.
(c) Firm 1 has a unit-cost equal to 300. With probability 50% firm 2 has a unit-cost equal to 450, but with probability 50% firm 2 has a unit-cost equal to 150. Assume we can analyze the interaction between firm 1 and 2 as a game with imperfect information. Find the quantities supplied by each firm (and each type of firm 2) in the Bayes-Nash equilibrium.