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 action and other players" action. 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 chooss , player 1 would can 14 Player 1, Player 2, Playor 3, and Player 4's earnings are listed in the other three tables. Player 1's earnings depend upon the action he chooses and the action player 4 chooses. Player 2's earnings depend upon the action he chooses and the action 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 Player 2's Payoffs Player 1's actions Player 3's Payoffs Player 2's actions Player 4's Payoffs Player 3's actions 12 16 14 |20 | 14 | 8 14 1843 8 20 12 a c 6108 c0 1616 c0 16 18 | 18 126 Game 2 Player 1's Payoffs Player 4's actions a* b* c* Player 2's Payoffs Player 1's actions Player 3's Payoffs Player 2's actions a b c* Player 4's Payoffs Player 3's actions a b c* 8 1210 2014 8141848 20| 12 12 16 14 c0 16160 16 18 |18 126 (a) (4 points) What would player 4 choose in Games 1 and 2 if he was fourth-order 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 G1G2 G1 G2 G1G2 Level 1 evel 2 Level 3 Level 4 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 action and other players" action. 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 chooss , player 1 would can 14 Player 1, Player 2, Playor 3, and Player 4's earnings are listed in the other three tables. Player 1's earnings depend upon the action he chooses and the action player 4 chooses. Player 2's earnings depend upon the action he chooses and the action 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 Player 2's Payoffs Player 1's actions Player 3's Payoffs Player 2's actions Player 4's Payoffs Player 3's actions 12 16 14 |20 | 14 | 8 14 1843 8 20 12 a c 6108 c0 1616 c0 16 18 | 18 126 Game 2 Player 1's Payoffs Player 4's actions a* b* c* Player 2's Payoffs Player 1's actions Player 3's Payoffs Player 2's actions a b c* Player 4's Payoffs Player 3's actions a b c* 8 1210 2014 8141848 20| 12 12 16 14 c0 16160 16 18 |18 126 (a) (4 points) What would player 4 choose in Games 1 and 2 if he was fourth-order 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 G1G2 G1 G2 G1G2 Level 1 evel 2 Level 3 Level 4