ECO 355 Game Theory I need a right answer of it QUESTION 7 P

ECO 355 Game Theory I need a right answer of it.

QUESTION 7 Player III Player II Player II PlayerI A 1,3,3 1,3,2 A 2,3,1 3,1,0 B 3.21 1.3.2 Player l B 3,1,0 0,0,4 The game above is a simulitaneous 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 Player 2 plays and Player 3 plays is a Nash Equilibrium profile.

Solution

Nash equilibrium:

Player 1 plays B (given player 3 plays E, B dominates A)

Player 2 plays D (given player 3 plays E, D weakly dominates C)

and Player 3 plays E (E strictly dominates F)