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Homework answers / question archive / Which one is false for the following three player game? Choice A for Player 3 L R T 3, 5, 3 2, 2, 3 M 1, 4, 2 4, 0, 0 B 2, 4, 1 1, 0, 8 Choice B for Player 3 L R T 2, 3, 5 4, 2, 6 M 1, 4, 3 1, 2, 1 B 2, 1, 1 3, 2, 6 A
Which one is false for the following three player game?
Choice A for Player 3
| L | R | |
| T | 3, 5, 3 | 2, 2, 3 |
| M | 1, 4, 2 | 4, 0, 0 |
| B | 2, 4, 1 | 1, 0, 8 |
Choice B for Player 3
| L | R | |
| T | 2, 3, 5 | 4, 2, 6 |
| M | 1, 4, 3 | 1, 2, 1 |
| B | 2, 1, 1 | 3, 2, 6 |
| A. |
Player 3 does not have a weakly dominated strategy |
|
| B. |
There is more than one outcome that survives the iterative elimination of strongly dominated strategies |
|
| C. |
(T,L,B) is the only outcome that survives the iterated elimination of strongly dominated strategies |
|
| D. |
Player 1 has a weakly dominated strategy |
A
L R
T 2, 3, 5 4, 2, 6
M 1, 4, 3 1, 2, 1
B 2, 1, 1 3, 2, 6
B
L R
T 3, 5, 3 2, 2, 3
M 1, 4, 2 4, 0, 0
B 2, 4, 1 1, 0, 8
For player 1 strategy T always dominates strategy B in both cases i.e. whether player 3 chooses A or B
Hence the reduced form of game will look like below
A B
L R
T 2, 3, 5 4, 2, 6
M 1, 4, 3 1, 2, 1
B
L R
T 3, 5, 3 2, 2, 3
M 1, 4, 2 4, 0, 0
for player 2 strategy L always dominates strategy R in both cases i.e. whether player 3 chooses A or B
Hence the reduced form of game will look like below
A
L
T 2, 3, 5
M 1, 4, 3
B
L
T 3, 5, 3
M 1, 4, 2
As more than one outcome survives
therfore now player 3 will always chooses A because the payoff from A is always higher than B
therefore Nash equilibrium is (T,L,A)
Hence option C is the answer
