Deck 11: Games and Decisions

Question 1

Is the following matrix game strictly determined?

Answer 1

False

Question 2

Is the following matrix game strictly determined?

Answer 2

True

Question 3

Is the following matrix game strictly determined?

Answer 3

True

Question 4

Is the following matrix game strictly determined?

Question 5

The matrix for a strictly determined matrix game is given below. Determine if the game is fair or not fair.

A) Fair
B) Not fair

Question 6

The matrix for a strictly determined matrix game is given below. Determine if the game is fair or not fair.

A) Fair
B) Not fair

Question 7

Find the saddle values, if it exists, for the matrix game (include row and column location).

A) 6; row 1 column 2
B) 4; row 1 column 1
C) 3; row 2 column 1
D) 4; row 2 column 1

Question 8

Find the saddle values, if it exists, for the matrix game (include row and column location).

A) 2; row 2 column 1
B) 2; row 3 column 2
C) 1; row 1 column 2
D) Does not exist

Question 9

Find the saddle values, if it exists, for the matrix game (include row and column location).

A) -5; row 1 column 2
B) 6; row 2 column 1
C) -2; row 3 column 2
D) -4; row 2 column 2

Question 10

Find the saddle values, if it exists, for the matrix game (include row and column location).

A) 0; row 3 column 4
B) 4; row 3 column 1
C) 0; row 1 column 2
D) 3; row 1 column 1

Question 11

Find the saddle value, if it exists, for the matrix game (include row and column location).

A) 1; row 1 column 3
B) 3; row 3 column 1
C) 1; row 3 column 2
D) 3; row 1 column 1

Question 12

What is the optimal strategy for each player in the following matrix game? Use R for row and C for column.

A) R plays row 2 or row 3, C plays column 1
B) R plays row 2, C plays column 4
C) R plays row 1 , C plays column 2
D) R plays row 1 or row 2, C plays column 1

Question 13

Daisy and Gus write down one of the numbers 1, 4 , or 7. If the sum of the numbers is even Daisy pays Gus that number of dimes. If the sum of the numbers is odd, Gus pays Daisy that number of dimes. Write Daisy's game matrix that corresponds to this situation.

A)
B)
C)
D)

Question 14

Find the saddle point and value of the game:

-Suppose a rugby team with the ball (team A) can choose from three plays while the opposing team (B) has four possible defenses. The numbers in the payoff matrix represent yards gained by A.

A) (3, 4), value 6
B) (1, 1), value 15
C) (2, 2), value 18
D) (2, 3), value 5

Question 15

Two countries are involved in a border war. Each country has 3 strategies with payoffs in square miles of land. Positive numbers represent gains by A.

A) (3, 2), value 5
B) (1, 3), value -10
C) (3, 3), value -10
D) (1, 3), value -8

Question 16

Two merchants in the same city plan on selling a new product. Each merchant has 3 strategies to enhance sales. The strategies chosen by each will determine the percentage of sales of the product each gets.

A) (1, 2), value -10
B) (1, 1), value -53
C) (2, 2), value 12
D) (3, 1), value -51

Question 17

Determine which row(s) and column(s) of the game matrix are recessive.

A)
B)
C)
D)

Question 18

Delete recessive rows and columns from the following matrix game:

A)
B)
C)
D)

Question 19

Delete recessive rows and columns from the following matrix game:

A)
B)
C)
D)

Question 20

Find the value of the game.

-

A)
B)
C)
D)

Question 21

Find the expected value of the matrix game M = for the respective row and column strategies:

A)
B)
C) -
D)

Question 22

Find the expected value of the matrix game M = for the respective row and column strategies:

A) 1
B)
C)
D)

Question 23

Find the expected value of the game matrix A = if player 1 and player 2 decide on strategies

A) 1
B)
C)
D)

Question 24

Find the expected value of the game matrix A = if player 1 and player 2 decide on strategies and Q = .

A)
B)
C)
D)

Question 25

Find the expected value of the game matrix A = if player 1 and player 2 decide on strategies and Q = .

A)
B)
C)
D)

Question 26

Solve the matrix game M = indicating optimal strategies and for R and C respectively, and the value v of the game.

A)
B)
C)
D)

Question 27

If a payoff matrix has a row consisting of all 0's, then that row is recessive.

Question 28

If a matrix game is fair, then both players have optimal strategies that are pure.

Question 29

In a two-finger Morra game, if player R matches player C, then R wins and if R and C don't match, then C wins. R will win $3 with one finger or two fingers, while C will win $1 with one finger and $5 with 2 fingers. The payoff matrix is Find the optimal strategies and for R and C respectively, and the value v of the game.

A)
B)
C)
D)

Question 30

Two supermarkets, R and C, want to run a promotional on the same item. A market research firm provided the payoff matrix below, where each entry indicates the percentage of customers going to market R at the indicated prices of that item. Find the saddle value, and the optimum strategy for each store.

A) 60%; R sells the item at $1.85, C sells the item at $1.55.
B) 60%; R sells the item at $1.55, C sells the item at $1.85.
C) 50%; R sells the item at $1.85, C sells the item at $1.55.
D) 50%; R sells the item at $1.55, C sells the item at $1.85.

Question 31

QMC decided to put its new product on the market with ads in a trade magazine and a booth at a trade show. It found out that its major competitor ZMC also had decided to advertise the same way for its new product. The payoff matrix shows the increased sales for QMC, as well as decreased sales for ZMC. What is the optimum strategy for QMC and the value of the game?

A) QMC should use ads with probabilityand use booths with probability . The value of the game is .
B) QMC should use ads with probabilityand use booths with probability . The value of the game is .

Question 32

Two Wally-Worlds are going to build within a three block area. The exact sites will determine the percentage of business above or below 50% each gets, as shown in the payoff matrix. What is the value of the game?

A) 12
B) 6
C) 8
D) 11

Question 33

Two racquetball clubs are in competition in attracting new members. Advertising campaigns are being contemplated by both clubs which emphasize either beginning, intermediate, or advanced player tournaments among members. After careful research, the following results were found:

Thus, if beginner tournaments are featured by both clubs, Club A expects to attract 25% of the new members and Club B expects to attract 75% of the new members, etc. Find the value of the game.

A) 55%
B) 85%
C) 45%
D) 65%

Question 34

The U.S. Marines is playing a war game with side A trying to capture side B's headquarters. Side A has three strategies and side B has four defenses. The payoff matrix shows side A's percentage chance of winning. What is the value of the game?

A) -75
B) -21
C) -41
D) 51

Question 35

Find the smallest integer k ? 0 such that adding k to each entry of the given matrix produces a matrix with all positive payoffs:

-

A) 4
B) 2
C) 1
D) 3

Question 36

Find the smallest integer k ? 0 such that adding k to each entry of the given matrix produces a matrix with all positive payoffs:

-

A) 3
B) 2
C) 0
D) 1

Question 37

Suppose a matrix game has the following nonstrictly determined matrix:

Set up (but do not solve), the two corresponding linear programming problem used to solve this matrix game.

A)
B)

Question 38

Suppose a matrix game has the following nonstrictly determined matrix:

Set up (but do not solve), the two corresponding linear programming problem used to solve this matrix game.

A)
B)

Question 39

Suppose a matrix game has the following nonstrictly determined matrix:

Set up (but do not solve), the two corresponding linear programming problem used to solve this matrix game.

A)
B)

Question 40

Solve the matrix game using a geometric linear programming approach.
M =

A)
B)
C)
D)

Question 41

If the value of a matrix game is positive, then all payoffs are positive.

Question 42

If M is a matrix game, then there is a fair matrix game in which the optimal strategies are those of M.

Question 43

A small town has two competing grocery stores, store R and store C. Each week each store decides to advertise its specials using either a newspaper advertisement or a mailing. The following payoff matrix indicates the percentage of market gain or loss for each choice of action by store R and store C.

Use linear programming and a geometric approach to find optimal strategies and for store R and store C and the value v of the game.

A)
B)
C)
D)

Question 44

Use the simplex method to find the optimum strategy for players A and B and the value of the game for the payoff matrix:

-

A)
B)
C)
D)

Question 45

Use the simplex method to find the optimum strategy for players A and B and the value of the game for the payoff matrix:

-

A)
B)
C)
D)

Question 46

Use the simplex method to find the optimum strategy for players A and B and the value of the game for the payoff matrix:

-

A)
B)
C)
D)

Question 47

Use the simplex method to find the optimum strategy for players A and B and the value of the game for the payoff matrix:

-

A)
B)
C)
D)

Question 48

A company has three different marketing strategies that produce different results depending upon whether inflation is above 6%, between 3% and 6% inclusive, or below 3% annually. The experts cannot predict inflation for the next year. The company has three plans of action and will implement these at varying percentages of its total operation. The payoff matrix for these three plans is given below, with values given in hundred thousands. What is the market strategy for the company that will yield the best expected value?

A) The company should use Plan 1 with probability 4/13, Plan 2 with probability 9/13, and Plan 3 with probability 0.
B) The company should use Plan 1 with probability 5/13, Plan 2 with probability 8/13, and Plan 3 with probability 0.
C) The company should use Plan 1 with probability 1, Plan 2 with probability 0, and Plan 3 with probability 0.
D) The company should use Plan 1 with probability 0, Plan 2 with probability 1, and Plan 3 with probability 0.

Question 49

A company has three different marketing strategies that produce different results depending upon whether inflation is above 6%, between 3% and 6% inclusive, or below 3% annually. The experts cannot predict inflation for the next year. The company has three plans of action and will implement these at varying percentages of its total operation. The payoff matrix for these three plans is given below, with values given in hundred thousands. What is the marketing strategy for the company that will yield the best expected value?

A) The company should use Plan 1 with probability 1/3, Plan 2 with probability 1/3, and Plan 3 with probability 1/3.
B) The company should use Plan 1 with probability 0, Plan 2 with probability 1, and Plan 3 with probability 0.
C) The company should use Plan 1 with probability 1, Plan 2 with probability 0, and Plan 3 with probability 0.
D) The company should use Plan 1 with probability 5/13, Plan 2 with probability 0, and Plan 3 with probability 8/13.

Question 50

A company has three products that fluctuate in favorability. The payoff matrix for the expected profit in tens of thousands of dollars is given below. What are the percentages of each product that the company should make that would maximize the expected value of the profit? Round to the nearest tenth of a percent, if necessary.

A) Product 1: 0%, Product 2: 100%, Product 3: 0%
B) Product 1: 38.5%, Product 2: 0%, Product 3: 61.5%
C) Product 1: 100%, Product 2: 0%, Product 3: 0%
D) Product 1: 33.3%, Product 2: 33.3%, Product 3: 33.3%

Question 51

A person has hired an investment broker to buy stock. The broker has three different stock funds that are of interest, but each is sensitive to a certain economic indicator that is impossible to predict. The indicator will be positive, neutral, or negative. The table below shows the payoffs in thousands of dollars. Find the strategy that the broker should recommend to maximize the expected value of the investment.

A) Invest in Stock A with probability 1, invest in Stock B with probability 0, and invest in Stock C with probability 0.
B) Invest in Stock A with probability 5/13, invest in Stock B with probability 8/13, and invest in Stock C with probability 0.
C) Invest in Stock A with probability 4/13, invest in Stock B with probability 9/13, and invest in Stock C with probability 0.
D) Invest in Stock A with probability 0, invest in Stock B with probability 1, and invest in Stock C with probability 0.

Question 52

A person is considering three different stocks, and each is sensitive to a certain economic indicator. The indicator will be positive, neutral, or negative, and fluctuate randomly. The payoffs are given in the table below, in thousands of dollars. What investment strategy should the person make to obtain the best expected value of profit?

A) Invest in Stock A with probability 1/3, invest in Stock B with probability 1/3, and invest in Stock C with probability 1/3.
B) Invest in Stock A with probability 5/13, invest in Stock B with probability 0, and invest in Stock C with probability 8/13.
C) Invest in Stock A with probability 0, invest in Stock B with probability 1, and invest in Stock C with probability 0.
D) Invest in Stock A with probability 1, invest in Stock B with probability 0, and invest in Stock C with probability 0.