Question

For the following matrix game, write down the equivalent LPPs for solving the game.

B

A= -1 2

1 0

Answer 1

1.

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

$E_1=-p_1+2p_2$

$E_2=p_1$

$-p_1+2p_2=p_1$

$p_2=1-p_1$

$p_1=p_2=0.5$

Substituting the values of p₁ and p₂ in equation E₂ :

$V=-0.5+2\cdot0.5=0.5$

2.

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

$L_1=-q_1+q_2$

$L_2=2q_1$

$-q_1+q_2=2q_1$

$q_2=1-q_1$

$3q_1=1-q_1$

$q_1=1/4, q_2=3/4$

Substituting the values of q₁ and q₂ in equation L₂ :

$V=-0.25+0.75=0.5$