Deck 9: Optimization Online Only

Question 1

Find all saddle points for the matrix game.

Answer 1

D

Question 2

Find all saddle points for the matrix game.

Answer 2

A

Question 3

Write the payoff matrix for the game.
In the traditional Japanese childrenʹs game janken (or ʺstone, scissors, paperʺ), at a given signal, each of two players shows either no fingers (stone), two fingers (scissors), or all five fingers
(paper). Stone beats scissors, scissors beats paper, and paper beats stone. In the case of a tie, there
Is no payoff. In the case of a win, the winner collects 50 yen.

Answer 3

B

Question 4

Find all saddle points for the matrix game.

Question 5

Find the value of the strategy.

Question 6

Find the value of the strategy.

Question 7

Find the value of the strategy.

Question 8

Write the payoff matrix for the game.
Player R has two cards: a red 2 and a black 7. Player C has three cards: a red 5, a black 6, and a black 10. They each show one of their cards. If the cards are the same color, C receives the larger of
The two numbers. If the cards are of different colors, R receives the sum of the two numbers.

Question 9

Find the expected payoff.

Question 10

Find the expected payoff.

Question 11

Write the payoff matrix for the game.
Players R and C each show 1, 2, or 3 fingers. If the total number N of fingers shown is even, then R pays N dollars to C. If N is odd, C pays N dollars to R.

Question 12

Find the expected payoff.

Question 13

Write the payoff matrix for the game.
Each player has a supply of nickels, dimes, and quarters. At a given signal, both players display one coin. If the displayed coins are not the same, then the player showing the higher valued coin
Gets to keep both. If they are both nickels or dimes, then player R keeps both; but if they are both
Quarters, then player C keeps both.

Question 14

Find all saddle points for the matrix game.

Question 15

Find the expected payoff.

Question 16

Write the payoff matrix for the game.
Each player has a supply of pennies, nickels, and dimes. At a given signal, both players display one coin. If the total number of cents N is even, then R pays N cents to C. If N is odd, then C pays
N cents to R.

Question 17

Find all saddle points for the matrix game.

Question 18

Find all saddle points for the matrix game.

Question 19

Find the value of the strategy.

Question 20

Find all saddle points for the matrix game.

Question 21

Solve the problem.
Player R has two cards: a red 2 and a black 8. Player C has three cards: a red 3, a black 5, and a black 10. They each show one of their cards. If the cards are the same color, C receives the larger of
The two numbers. If the cards are of different colors, R receives the sum of the two numbers. The
Payoff matrix is :

Question 22

Solve the problem.

Question 23

Find the value of the matrix game.

Question 24

Find the value of the matrix game.

Question 25

Solve the problem.
Each player has a supply of nickels, dimes, and quarters. At a given signal, both players display one coin. If the displayed coins are not the same, then the player showing the higher valued coin
Gets to keep both. If they are both nickels or dimes, then player R keeps both; but if they are both
Quarters, then player C keeps both. Find the optimal strategy for player C.

Question 26

Find the optimal row or column strategy of the matrix game.

Question 27

Find the value of the matrix game.

Question 28

Find the optimal row or column strategy of the matrix game.

Question 29

Find the optimal row or column strategy of the matrix game.

Question 30

Solve the problem.
Player R has two cards: a red 2 and a black 8. Player C has three cards: a red 3, a black 5, and a black 10. They each show one of their cards. If the cards are the same color, C receives the larger of
The two numbers. If the cards are of different colors, R receives the sum of the two numbers. The
Payoff matrix is :

Question 31

Solve the problem.

Question 32

Find the optimal row or column strategy of the matrix game.

Question 33

Find the value of the strategy.
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Question 34

Find the optimal row or column strategy of the matrix game.

Question 35

Find the optimal row or column strategy of the matrix game.

Question 36

Find the value of the strategy.

Question 37

Find the optimal row or column strategy of the matrix game.

Question 38

Find the optimal row or column strategy of the matrix game.

Question 39

Solve the problem.

Question 40

Find the value of the matrix game.

Question 41

Solve the problem.
If the payoff matrix of a matrix game contains a saddle point, what is the optimal strategy for the column player?

A)Always choose the column with the largest maximum.
B)Always choose the column with the smallest maximum.
C)Always choose the column with the smallest minimum.
D)Always choose the column with the largest minimum.

Question 42

Determine whether the statement is true or false.
In a matrix game, the value ν(y)of a particular strategy y to player C is equal to the minimum of
the inner product of y with each of the rows of the payoff matrix A.

Question 43

Solve the problem.
In a matrix game with payoff matrix A, how can you find the value ν(x)of a strategy x to row player R?

A)ν(x)is the minimum of the inner product of x with each of the columns of A.
B)ν(x)is the maximum of the inner product of x with each of the columns of A.
C)ν(x)is the maximum of the inner product of x with each of the rows of A.
D)ν(x)is the minimum of the inner product of x with each of the rows of A.

Question 44

Determine whether the statement is true or false.
In a matrix game, if row s is dominant to some other row in payoff matrix A, then row s will not be
used in some optimal strategy for row player R.

Question 45

Solve the problem.
Anne and Michael are playing a game in which each player has a choice of two colors: green or blue. The payoff matrix with Anne as the row player is given below:

Question 46

Determine whether the statement is true or false.
The value νC of a matrix game to player C is the maximum of the values of the various possible
strategies for C.

Question 47

Solve the problem.
If the payoff matrix of a matrix game contains a saddle point, what is the optimal strategy for the 45) row player?

A)Always choose the row with the largest maximum.
B)Always choose the row with the smallest minimum.
C)Always choose the row with the smallest maximum.
D)Always choose the row with the largest minimum.

Question 48

Solve the problem.

Question 49

Solve the problem.
In a matrix game with payoff matrix A, how can you find the value ν(y)of a strategy y to player C?

A)ν(y)is the maximum of the inner product of y with each of the columns of A.
B)ν(y)is the minimum of the inner product of y with each of the columns of A.
C)ν(y)is the maximum of the inner product of y with each of the rows of A.
D)ν(y)is the minimum of the inner product of y with each of the rows of A.

Question 50

Solve the problem.

Question 51

Solve the problem.

Question 52

Determine whether the statement is true or false.
If the payoff matrix of a matrix game contains a saddle point, the optimal strategy for each player
will be a pure strategy.

Question 53

Solve the problem.
In certain situations, a matrix game can be reduced to a smaller game by deleting certain rows and/or columns from the payoff matrix. The optimal strategy for the reduced game will then
Determine the optimal strategy for the original game. In what circumstances may a row or column
Be deleted from the payoff matrix?

A)A row may be deleted if it is recessive to some other row and a column may be deleted if it is recessive to some other column.
B)A row may be deleted if it is dominant to some other row and a column may be deleted if it is recessive to some other column.
C)A row may be deleted if it is dominant to some other row and a column may be deleted if it is dominant to some other column.
D)A row may be deleted if it is recessive to some other row and a column may be deleted if it is dominant to some other column.

Question 54

Determine whether the statement is true or false.
If the payoff matrix of a matrix game contains a saddle point, the optimal strategy for the row
player will be to always choose the row with the largest minimum while the optimal strategy for
the column player will be to always choose the column with the smallest maximum.

Question 55

Solve the problem.