Question

Using graphical method, solve the game whose pay-off matrix is given as:

Player B

I II III IV

Player A I 1 3 -3 7

II 2 5 4 -6

Answer 1

Column MiniMax =2

Row MaxiMin =-3

1.

The point of optimal solution occurs at the intersection of two lines:

$E_1=p_1-3p_2$

$E_3=2p_1+4p_2$

$p_1-3p_2=2p_1+4p_2$

$p_2=1-p_1$

$1-4p_2=2+2p_2$

$p_2=-1/6$ $,p_1=7/6$

$V=7/6+3/6=5/3$

2.

The point of optimal solution occurs at the intersection of two lines:

$L_1=q_1+2q_2$

$L_3=-3q_1+4q_2$

$q_1+2q_2=-3q_1+4q_2$

$q_2=1-q_1$

$1+q_2=-3+7q_2$

$q_2=2/3$ $,q_1=1/3$

$V=1/3+4/3=5/3$