2. (20%)

Find the Nash equilibria in the following three-player game, showing clearly why what you choose is a Nash equilibrium:

(Player 1 chooses a or b, Player 2 chooses L or R, Player 3 chooses A,B or C.

In each entry, the payoffs are in the order of 1,2,3.)

If Player 3 chooses A,

L R

a 2,1,1 0,0,0

b 0,0,0 1,1,2

.

If Player 3 chooses B,

L R

a 2,1,2 0,2,0

b 1,1,0 1,2,1

If Player 3 chooses C,

L R

a 1,2,0 0,1,2

b 0,1,0 2,0,0