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?

Homework Answers

Answer #1
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

Know the answer?
Your Answer:

Post as a guest

Your Name:

What's your source?

Earn Coins

Coins can be redeemed for fabulous gifts.

Not the answer you're looking for?
Ask your own homework help question
Similar Questions
Consider the following two-person zero-sum game. Assume the two players have the same two strategy options....
Consider the following two-person zero-sum game. Assume the two players have the same two strategy options. The payoff table shows the gains for Player A. Player B Player A strategy b1 strategy b2 strategy a1 3 9 Strategy a2 6 2 Determine the optimal strategy for each player. What is the value of the game?
Find the optimal strategies and the value of the game. Indicate whether it is a fair...
Find the optimal strategies and the value of the game. Indicate whether it is a fair or a strictly determinable game: b1 b2 b3 b4 a1 2 10 7 0 a2 3 4 9 -1 a3 -6 -3 11 -3 a4 8 5 -4 -5
24. Two players are engaged in a game of Chicken. There are two possible strategies: swerve...
24. Two players are engaged in a game of Chicken. There are two possible strategies: swerve and drive straight. A player who swerves is called Chicken and gets a payoff of zero, regardless of what the other player does. A player who drives straight gets a payoff of 432 if the other player swerves and a payoff of −48 if the other player also drives straight. This game has two pure strategy equilibria and a. a mixed strategy equilibrium in...
[Game Theory] Define a zero-sum game in which one player’s unique optimal strategy is pure and...
[Game Theory] Define a zero-sum game in which one player’s unique optimal strategy is pure and all of the other player’s optimal strategies are mixed.
4 A) Considering the following two-person zero-sum game, what percentage of the time should the row...
4 A) Considering the following two-person zero-sum game, what percentage of the time should the row player play strategy X2?                                                                                                             Y1             Y2                                                X1            6                3                                                X2            2                8 A. 1/3 B. 2/3 C. 4/9 D. 5/9 4 B) Considering the following two-person zero-sum game, what percentage of the time should the column player play strategy Y1?                                                              Y1              Y2                                                X1           6                 3                                                X2           2                 8 A. 1/3 B. 2/3 C. 4/9 D. 5/9 4...
Two players can name a positive integer number from 1 to 6. If the sum of...
Two players can name a positive integer number from 1 to 6. If the sum of the two numbers does not exceed 6 each player obtains payoff equal to the number that the player named. If the sum exceeds 6, the player who named the lower number obtains the payoff equal to that number and the other player obtains a payoff equal to the difference between 6 and the lower number. If the sum exceeds 6 and both numbers are...
Recall the Lions and Antelopes game. This time there are two lions and three antelopes. The...
Recall the Lions and Antelopes game. This time there are two lions and three antelopes. The sizes (values) of the antelopes are A1 > A2 > A3. As before, if two lions chase the same antelope they each get half. If they chase different antelopes they each get the one they chase. (a) Write down the game payoff matrix. (b) Show that if A2 < A1/2 then chasing antelope 1 is an ESS. (c) Now suppose A2 > A1/2 and...
solve the two person zero sum game with the payoff matrix: -1 -1/2 1/2 1 4/3...
solve the two person zero sum game with the payoff matrix: -1 -1/2 1/2 1 4/3 1 -2/3 -1
(4) In this game, each of two players can volunteer some of their spare time planting...
(4) In this game, each of two players can volunteer some of their spare time planting and cleaning up the community garden. They both like a nicer garden and the garden is nicer if they volunteer more time to work on it. However, each would rather that the other person do the volunteering. Suppose that each player can volunteer 0, 1, 2, 3, or4 hours. If player 1 volunteers x hours and 2 volunteers y hours, then the resultant garden...
Mixed Strategies Consider the following game between two players Bad-Boy and Good-Girl. Bad-Boy can either behave...
Mixed Strategies Consider the following game between two players Bad-Boy and Good-Girl. Bad-Boy can either behave or misbehave whereas Good-Girl can either punish or reward. Below payoff matrix shows the game as pure strategies. Good Girl Reward Punish Bad Boy Behave 5, 5 -5,-5 Misbehave 10,-10 -10,-5 Question 41 (1 point) What is the Nash equilibrium of the game in pure strategies? Question 41 options: Behave-Reward Behave-Punish Misbehave-Punish There is no Nash equilibrium in pure strategies. Question 42 (1 point)...
ADVERTISEMENT
Need Online Homework Help?

Get Answers For Free
Most questions answered within 1 hours.

Ask a Question
ADVERTISEMENT
Active Questions
  • A) i) The voltage across a Zener diode is not constant. How do you characterize the...
    asked 9 minutes ago
  • Aumented Matrix using elimination method for solving a system of linear equations. Apply row operations to...
    asked 21 minutes ago
  • The past twenty years have seen advancements in technology that were critical to further understanding concepts...
    asked 30 minutes ago
  • What is the SPOT position of a wheat user/consumer like Pillsbury? What is the appropriate forward/futures...
    asked 38 minutes ago
  • Summative evaluations frequently include __________________ A) Time to mastery. B) Cost of program development. C) Functionality...
    asked 45 minutes ago
  • Child abuse occurs in that type of family environments? A) step families B) low income families...
    asked 1 hour ago
  • A disk with a c value of 1/2, a mass of 4 kg, and radius of...
    asked 1 hour ago
  • 1. Modern couples in the United States are having fewer children. a. True b. False 2.According...
    asked 1 hour ago
  • Assume the following information regarding U.S. and European annualized interest rates: Currency                          &n
    asked 2 hours ago
  • What is the basis of reliability for the following: 1)Dying declaration 2) business records 3)excited utterness...
    asked 2 hours ago
  • P6-9 (L02,4) (Analysis of Business Problems) James Kirk is a financial executive with McDowell Enterprises. Although...
    asked 2 hours ago
  • Written story about someone who engages in primary deviance and then becomes a secondary deviant. Make...
    asked 2 hours ago