2. (25 %) Consider the following two-person zero-sum game. Assume the two player

Question

2. (25 %) 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

  5

-2

Strategy  a2

-2

-1

  2

Strategy  a3

  2

  1

-5

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?

ANS:  

There is not an optimal pure strategy.

However, there are dominated strategies.

Strategy a3 is dominated (by strategy a1) and can be eliminated.

Then strategy b1 is dominated (by strategy b2) and can be eliminated.

Now it is a 2 x 2 game.

Mixed-strategy probabilities are found algebraically: p = .3, (1 - p) = .7, q = .4, (1 - q) = .6

Value of game = 0.8

  

     

Player B

     

Player A

     

Strategy b1

     

Strategy b2

     

Strategy b3

     

Strategy  a1

     

  3

     

  5

     

-2

     

Strategy  a2

     

-2

     

-1

     

  2

     

Strategy  a3

     

  2

     

  1

     

-5

  

Explanation / Answer

no there is no optimal pure strategy.

but there are dominated strategies.

Strategy a3 is dominated by strategy a1 and can be eliminated.

Then strategy b1 is dominated by strategy b2 and can be eliminated.

Now it is a 2 x 2 game.

Mixed-strategy probabilities are found algebraically: p = .3, (1 - p) = .7, q = .4, (1 - q) = .6

Value of game = 0.8

Related Questions

Navigate

• Browse (All)
• Browse 2
• Subjects

---

---

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.