3. Consider two firms playing a two-stage game with discount factor 8. In the first stage they play a Cournot quantity setting game where each firm has costs c;(qi) = 10g; for i E {1,2} and the demand is given by p(q) = 100 q where q = q1 + q2. In the second stage, after the results of the Cournot game are observed, the firms play the following game: Player 2 a Player 1 A 100,100 0,0 0,0 300,300 (1) Find the unique Nash equilibrium of the first stage game and the two pure strategy Nash equilibria of the second stage game. (2) As far as the two firms are considered, what are the nmetric Pareto optimal outcomes of each stage game? (3) For which values of 8 can the Pareto optimal outcomes be supported as a subgame perfect equilibrium? (4) Assume that 8 = 0.5. What is the "best" symmetric subgame perfect equilibrium that the players can support?