Consider the following two-person zero-sum game. Assume the two players have the
ID: 334192 • Letter: C
Question
Consider the following two-person zero-sum game. Assume the two players have the same three strategy options. The payoff table below shows the gains for Player A.
Player B
Player A
Strategy b1
Strategy b2
Strategy b3
Strategy a1
3
2
?4
Strategy a2
?1
0
2
Strategy a3
4
5
?3
Is there an optimal pure strategy for this game? If so, what is it? If not, can the mixed-strategy probabilities be found algebraically? What is the value of the game?
Player B
Player A
Strategy b1
Strategy b2
Strategy b3
Strategy a1
3
2
?4
Strategy a2
?1
0
2
Strategy a3
4
5
?3
Explanation / Answer
The value of the game lies between -1 and 2
As you can see there is no pure strategy for the game we have to find the optimal solution algebraical method or linear programming method
Player A linear program
Maximize Z = v
Subject to
v-3x1+x2-4x3<=0
v-2x1+0x2-5x3<=0
v+4x1-2x2+3x3<=0
x1,x2,x3>=0 , v is unrestricted
For B linear program
Minimize Z= v
Subject to
v-3y1-2y2+4y3>=0
v+y1+0y2-2y3>= 0
c-4y1-5y2+3y3>=0, v is unrestricted
Optimal value of game lies between -1 to 2
B b1 b2 b3 Row minimum A a1 3 2 -4 -4 a2 -1 0 2 -1 Maximin a3 4 5 -3 -3 Column Maximum 4 5 2 Minimax