Augmented Competition: Consider two firms playing a two-stage game with discount factor . In the first stage they play a Cournot quantity-setting game in which each firm has costs ci(qi) = 10qi for i {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 standardsetting game:

a. Find the unique Nash equilibrium of the first-stage game and the two pure-strategy Nash equilibria of the second-stage game.

b. As far as the two firms are considered, what are the symmetric Paretooptimal outcomes of each stage-game?

c. For which values of can the Pareto-optimal outcomes be supported as a subgame-perfect equilibrium?

d. Assume that = 0.5. What is the "best" symmetric subgame-perfect equilibrium that the players can support? e. What happens to the best symmetric subgame-perfect equilibrium that the players can support as drops toward zero?