QUESTION Player III Player II Player II A 133 132 B 310004 A

QUESTION Player III Player II Player II A 1,3,3 1,3,2 B 3,1,00,0,4 A 2,3,1 3,1,0 B 3,2,-1 1,3,2 Player l Player I The game above is a simultaneous three player game between players 1, 2, and 3. Player 1 chooses between A and B, Player 2 between C and D and Player 3 between E and F. In the game above, the strategy profile in which Player 1 plays , and Player 3 plays is a Nash Equilibrium profile.

Solution

In the above game Given that player 3 chooses E then ,when player 1 chooses A then , player 2 is indifferent between D and C. And when player 1 chooses B then, player 2 chooses D. And when player 2 chooses D then, player 1 chooses B .And when player 2 chooses C then, player 1 chooses A.

Similarly Given that player 3 chooses F , then when player 1 chooses A then, player2 chooses D . And when player 1 chooses B then, player 2 chooses C. And when player 2 chooses D then, player 1 chooses B . And when player 2 chooses C then, player 1 chooses A.

Therefore, given player 3 strategy , nash equilibrium is [B,D] but now player 3 has more pay-off in choosing E.

Therefore, in the game above, the strategy profile in which player1 plays B , player 2 plays D and player 3 plays E is a nash equilibrium profile.