Q. a) Solve a standard Cournot game between player 1 and 2 with the following demand and cost functions: P = 100 q1 q2 and Ci(qi) = 2qi for i = 1, 2. b) Assume now that firm 1 is a Stackelberg leader. The new timing is 1. Player 1 chooses its output q1. 2. Player 2 observes q1. 3. Player 2 chooses q2. What is the SPNE? c) Consider this alternative timing. Suppose now that player 1 is given the opportunity to adjust its output AFTER player 2 has chosen its output. Should player 1 accept this opportunity and adjust its output? Why? (Assume that none of the players anticipated this opportunity when choosing their output). New timing: T = 1: Player 1 chooses its output q1. T = 2: Player 2 observes q1. T = 3: Player 2 chooses its output q2. T = 4: Player 1 is given the opportunity to adjust its output: q1. T = 5: The payoffs are realized. d) Consider another alternative timing. Now suppose that, BEFORE player 2 has chosen its output, player is 1 is given the oppor- tunity to adjust its output AFTER player 2 has chosen its output. Should player 1 accept this opportunity in T=4 and adjust its output in T = 6? Why? New timing: T = 1: Player 1 chooses its output q1. T = 2: Player 2 observes q1. T = 3: Player 1 is given the opportunity to adjust its output in T = 6. T = 4: Player 1 accepts or rejects this opportunity. T = 5: Player 2 observes player 1's choice in T = 4 and chooses its output q2. T = 6: Player 1 adjusts its output, q1, only if he accepted the opportunity in T = 4. T = 7: The payoffs are realized.