ECO 6900 Problem Set 2
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ECO 6900
Problem Set 2.
Due on December 5, 2022
Instructions:
● Your answers have to be uploaded to Crowdmark before 11:59 PM. No exceptions.
● You may work together, but everyone must write up the answers individually.
● When you are asked to explain or discuss various issues, you will get a higher mark by providing a short answer that gets right to the point instead of discussing generalities without explicitly answering the question you are asked about.
● Before submitting your assignment, make sure the pages are in the order and rotated correctly. Otherwise I may deduct some points.
● Always show your work.
Question 1
Suppose that you run an experiment in which participants play Game 1 and Game 2 displayed below. Participants’ earnings depend on the combination of their actions and other players’ actions. These earnings possibilities are represented in the tables below. For example, in Game 1, if player 1 chooses a and player 4 chooses b, player 1 would earn 16 dollars. If instead player 4 chooses c, player 1 will earn 14 dollars. Player 1, Player 2, Player 3, and Player 4’s earnings are listed in three other tables. Player 1’s earnings depend on the action he chooses, and player 4 chooses. Player 2’s earnings depend on the action he chooses, and player 1 chooses. Player 3’s earnings depend upon the action he chooses and the action Player 2 chooses. Player 4’s earnings depend upon the action he chooses and the action Player 3 chooses. For example, if player 1 chooses c, player 2 chooses b, player 3 chooses a, and player 4 chooses b, then player 1 would earn 10 dollars, player 2 would earn 18 dollars, player 3 would earn 18 dollars, and player 4 would earn 0 dollars.
Game 1
|
Player 1's Payoffs Player 4's actions a b c |
Player 2's Payoffs Player 1's actions a b c |
Player 3's Payoffs Player 2's actions a b c |
Player 4's Payoffs Player 3's actions a b c |
||||||||||||
|
b
c |
12 |
16 |
14 |
b
c |
20 |
14 |
8 |
b
c |
14 |
18 |
4 |
b
c |
8 |
20 |
12 |
|
8 |
12 |
10 |
16 |
2 |
18 |
20 |
8 |
14 |
0 |
8 |
16 |
||||
|
6 |
10 |
8 |
0 |
16 |
16 |
0 |
16 |
18 |
18 |
12 |
6 |
||||
Game 2
|
Player 1's Payoffs Player 4's actions a* b* c* |
Player 2's Payoffs Player 1's actions a* b* c* |
Player 3's Payoffs Player 2's actions a* b* c* |
Player 4's Payoffs Player 3's actions a* b* c* |
||||||||||||
|
*
* |
8 |
12 |
10 |
*
* |
20 |
14 |
8 |
*
* |
14 |
18 |
4 |
*
* |
8 |
20 |
12 |
|
6 |
10 |
8 |
16 |
2 |
18 |
20 |
8 |
14 |
0 |
8 |
16 |
||||
|
12 |
16 |
14 |
0 |
16 |
16 |
0 |
16 |
18 |
18 |
12 |
6 |
||||
(a) (4 points) What would player 4 choose in Games 1 and 2 if he was fourth-order rational (i.e. she is rational, she believes the other players are rational, and she believes that Player 3 believes that Player 2 believes that Player 1 is rational....)?
(b) (16 points) Suppose that you would like to classify subjects based on the Level-k model. Fill out the following table. Here, G1 refers to the choice made by a player in Game 1 (a; b;or c) and G2 refers to the choice made by a player in Game 2 (a* ; b* ;or c* ). (Hint: Remember that according to the Level-k model, a Level 0 player would randomize between available choices, a Level 1 player would best respond to a Level 0 player, and so on.)
|
|
Player 1 |
Player 2 |
Player 3 |
Player 4 |
||||
|
G1 |
G2 |
G1 |
G2 |
G1 |
G2 |
G1 |
G2 |
|
|
Level 1 |
a |
|
a |
|
b |
|
a |
|
|
Level 2 |
a |
|
a |
|
b |
|
a |
|
|
Level 3 |
a |
|
a |
|
b |
|
a |
|
|
Level 4 |
a |
|||||||
2022-12-06