Question

2. Consider the following game. | 1 2 | H | M | L | | :--- | :--- | :--- | :--- | | H | 6, 6 | 0, 10 | 0, 8 | | M | 10, 0 | 5, 5 | 0, 8 | | L | 8, 0 | 8, 0 | 4, 4 | (a) Find all Nash equilibria in pure strategies. (b) Suppose that the above game is player twice. Identify all Subgame Perfect equilibria. (c) Suppose that the above game is played infinitely many times, and each player discount future profit with a discount factor of ? ? [0,1) (i.e., $1 in period t + 1 is worth $? in period t). Construct the SPE strategies of the resulting repeated game that could sustain (H, H) in every period for a sufficiently large ?. What is the minimal value of ? ? [0,1) necessary for this result? 3. Consider the Cournot game we discussed in the class: Two firms, 1 and 2,

          2. Consider the following game.

| 1  2 | H | M | L |
| :--- | :--- | :--- | :--- |
| H | 6, 6 | 0, 10 | 0, 8 |
| M | 10, 0 | 5, 5 | 0, 8 |
| L | 8, 0 | 8, 0 | 4, 4 |

(a) Find all Nash equilibria in pure strategies.
(b) Suppose that the above game is player twice. Identify all Subgame Perfect equilibria.
(c) Suppose that the above game is played infinitely many times, and each player discount future profit with a discount factor of ? ? [0,1) (i.e., $1 in period t + 1 is worth $? in period t). Construct the SPE strategies of the resulting repeated game that could sustain (H, H) in every period for a sufficiently large ?. What is the minimal value of ? ? [0,1) necessary for this result?
3. Consider the Cournot game we discussed in the class: Two firms, 1 and 2,

2. Consider the following game.

| 1 2 | H | M | L |
| :— | :— | :— | :— |
| H | 6, 6 | 0, 10 | 0, 8 |
| M | 10, 0 | 5, 5 | 0, 8 |
| L | 8, 0 | 8, 0 | 4, 4 |

(a) Find all Nash equilibria in pure strategies.
(b) Suppose that the above game is player twice. Identify all Subgame Perfect equilibria.
(c) Suppose that the above game is played infinitely many times, and each player discount future profit with a discount factor of ? ? [0,1) (i.e., 1 in period t + 1 is worth? in period t). Construct the SPE strategies of the resulting repeated game that could sustain (H, H) in every period for a sufficiently large ?. What is the minimal value of ? ? [0,1) necessary for this result?
3. Consider the Cournot game we discussed in the class: Two firms, 1 and 2,

Added by Nicole P.

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