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

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