9.1 Multistage Practice: Consider the following simultaneous-move game that is played twice (the players observe the first-period outcome prior to the second- period play): Player 2 L C R T 10, 10 2, 12 0, 13 Player 1 M 12, 2 5, 5 0, 0 B 13, 0 0, 0 1, 1 9.7 Exercises . 187 2 2 (3, 3) C C N n N n (1, 1) (0, 3) (2, 2) (1, 4) FIGURE 9.2 The Centipede Game. a. Find all the pure-strategy subgame-perfect equilibria with no discount- ing (8 = 1). Be precise in defining history-contingent strategies for both players. b. For each of the equilibria you found in (a), find the smallest discount factor that supports it.9.6 Augmented Competition: Consider two firms playing a two-stage game with discount factor 8. In the first stage they play a Cournot quantity-setting game in which each firm has costs c; (q;) = 10q; for i e {1, 2) and the demand is given by p(q) = 100 - q, where q = q1 + 92. In the second stage, after the results of the Cournot game are observed, the firms play the following standard- setting game: Player 2 a b A 100, 100 0, 0 Player 1 B 0, 0 300, 300 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 Pareto- optimal 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 8 = 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?10.2 Grim Trigger: Consider the innitely repeated game with discount factor 6