Question

# Consider the following two-person zero-sum game. Assume the two players have the same three strategy options....

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?

 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

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

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