FInd all the Nash Equilibria in these games 10 Player 1 choo

FInd all the Nash Equilibria in these games.

10) Player 1 chooses row Player 2 chooses column Player 3 chooses matrix 3.-2.-1 10.a) 1.2.3) 1.-2.-3 3.-2.-1

Solution

If Matrix 1 is chose by Player 3 then NE available in this payoff matrix is (1,2,3) & (3,2,1)[ Because Player 1 will choose row 1 if player 2 plays 1st column (1>1)& whill choose row 1 again if player 2 chooses 2nd column (3>-3).

Similarly Player 2 is indifferent between both columns as he will have same payoff in each cases.

On the same line in 2nd matrix we have NE (1,2,3) & (3,2,1) as completely same logic follows

Total NE are 4 and those will be (row1,column1) & (row1,column2) in Matrix 1 ; (row2,column1) & (row2,column2)