Question 1

For a truel where the choices are sequential, which statement is true?

Accepted Answer

A)  The game tree has three termination nodes. 
B)  The game tree has five termination nodes. 
C)  The game tree has six termination nodes. 
D)  The game tree has nine termination nodes. 
A)  The game tree has three termination nodes. 
B)  The game tree has five termination nodes. 
C)  The game tree has six termination nodes. 
D)  The game tree has nine termination nodes.

Question 2

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to the column player II. 
$\left[ \begin{array} { l l } 
5 & 2 \
2 & 1
\end{array} \right]$
 Which of the following statements is true?

Accepted Answer

A)  The game has no saddlepoint. 
B)  The game has a saddlepoint; the value of the game is 1. 
C)  The game has a saddlepoint; the value of the game is 2. 
D)  The game has a saddlepoint; the value of the game is 5. 
A)  The game has no saddlepoint. 
B)  The game has a saddlepoint; the value of the game is 1. 
C)  The game has a saddlepoint; the value of the game is 2. 
D)  The game has a saddlepoint; the value of the game is 5.

Question 3

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to the column player II. Which of the following statements is true? 
$\left[ \begin{array} { l l } 
5 & 2 \
2 & 1
\end{array} \right]$

Accepted Answer

A)  The maximin strategy of player I is to always play the first row; the minimax strategy of player II is to always play the first column. 
B)  The maximin strategy of player I is to always play the second row; the minimax strategy of player II is to always play the first column. 
C)  The maximin strategy of player I is to always play the first row; the minimax strategy of player II is to always play the second column. 
D)  The maximin strategy of player I is to always play the second row; the minimax strategy of player II is to always play the second column. 
A)  The maximin strategy of player I is to always play the first row; the minimax strategy of player II is to always play the first column. 
B)  The maximin strategy of player I is to always play the second row; the minimax strategy of player II is to always play the first column. 
C)  The maximin strategy of player I is to always play the first row; the minimax strategy of player II is to always play the second column. 
D)  The maximin strategy of player I is to always play the second row; the minimax strategy of player II is to always play the second column.

Question 4

Construct the game tree for a truel played sequentially, for which the outcomes have the following payoffs. What are the optimal strategies for this game? 
$\begin{array}{rr}
\text {Sole survivor }&\text { 4 point }\
\text {One of two survivors }&\text { 3 point }\
\text {One of three survivors}&\text { 2 point }\
\text {Nonsurvivor}&\text { 1 point }\
\end{array}$

Accepted Answer

The answer of Construct the game tree for a truel...

Question 5

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to column player II.   The maximin strategy of player I is:

Accepted Answer

A)  to always play the first row. 
B)  to always play the second row. 
C)  to always play the third row. 
D)  to play two or more of the rows. 
A)  to always play the first row. 
B)  to always play the second row. 
C)  to always play the third row. 
D)  to play two or more of the rows.

Question 6

Create a three-by-three matrix that represents a two-person zero-sum game in which each player has three options and at least one player has a dominated strategy.

Accepted Answer

Answers may vary. For example,

Question 7

For a truel where the choices are sequential, which statement is true?

Accepted Answer

A)  The game tree has no cut branches. 
B)  The game tree has two cut branches. 
C)  The game tree has four cut branches. 
D)  The game tree has six cut branches. 
A)  The game tree has no cut branches. 
B)  The game tree has two cut branches. 
C)  The game tree has four cut branches. 
D)  The game tree has six cut branches.

Question 8

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to column player II.   The minimax strategy of player II is:

Accepted Answer

A)  to always play the first column. 
B)  to always play the second column. 
C)  to always play the third column. 
D)  to play two or more of the columns. 
A)  to always play the first column. 
B)  to always play the second column. 
C)  to always play the third column. 
D)  to play two or more of the columns.

Question 9

The game of Prisoner's Dilemma is an example of: 
I: a variable-sum game.
II: a partial-conflict game.

Accepted Answer

A)  I only 
B)  II only 
C)  both I and II 
D)  neither I nor II 
A)  I only 
B)  II only 
C)  both I and II 
D)  neither I nor II

Question 10

Create a three-by-three matrix that represents a two-person zero-sum game in which each player has three options and the game has no saddlepoint.

Accepted Answer

Answers may vary. For example,

Question 11

Consider the following partial-conflict game played in a noncooperative manner.   Which of the following statements is true?

Accepted Answer

A)  The dominant strategy for player I is to select choice A. 
B)  The dominant strategy for player I is to select choice B. 
C)  Player I has no dominant strategy. 
A)  The dominant strategy for player I is to select choice A. 
B)  The dominant strategy for player I is to select choice B. 
C)  Player I has no dominant strategy.

Question 12

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to column player II.   Does this game have a saddlepoint? What is each player's minimax or maximin strategy? Justify your response.

Accepted Answer

It has a saddlepoint

Question 13

Consider the following partial-conflict game played in a noncooperative manner. The first payoff is to player I; the second is to player II. $$\begin{array} { l c c } 
& \text { Player II } & \
\text { Player I } & \text { Choice A } & \text { Choice B } \
\text { Choice A } & ( 1,1 ) & ( 2,6 ) \
\text { Choice B } & ( 6,2 ) & ( 5,5 )
\end{array}$$ What outcomes constitute a Nash equilibrium?

Accepted Answer

A)  only when both players select A 
B)  only when both players select B 
C)  only when one player selects A and the other selects B 
D)  only when both players select A or both players select B 
A)  only when both players select A 
B)  only when both players select B 
C)  only when one player selects A and the other selects B 
D)  only when both players select A or both players select B

Question 14

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to column player II.   Does this game have a saddlepoint? What is each player's minimax or maximin strategy? Justify your response.

Accepted Answer

It has no saddlepoin

Question 15

You can choose to buy an extended warranty for your computer for $200. During this period, you will experience either a minor ($100) or major ($500) repair bill. If you buy the warranty, you will not have to pay the repair bill. Assume the company wants to make as much money as possible, and you wish to spend as little as possible. Which of the following is a true statement?

Accepted Answer

A)  This game has no saddlepoint. 
B)  This game has a saddlepoint; the value of the game is $100. 
C)  This game has a saddlepoint; the value of the game is $200. 
D)  This game has a saddlepoint; the value of the game is $500. 
A)  This game has no saddlepoint. 
B)  This game has a saddlepoint; the value of the game is $100. 
C)  This game has a saddlepoint; the value of the game is $200. 
D)  This game has a saddlepoint; the value of the game is $500.

Question 16

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to column player II. 
$\begin{array} { l l l } 
3 & 7 & 2 \
1 & 4 & 6 \
9 & 5 & 8
\end{array}$ 
Which of the following statements is true?

Accepted Answer

A)  The game has no saddlepoint. 
B)  The game has a saddlepoint; the value of the game is 4. 
C)  The game has a saddlepoint; the value of the game is 5. 
D)  The game has a saddlepoint; the value of the game is 6. 
A)  The game has no saddlepoint. 
B)  The game has a saddlepoint; the value of the game is 4. 
C)  The game has a saddlepoint; the value of the game is 5. 
D)  The game has a saddlepoint; the value of the game is 6.

Question 17

Construct the game tree for a truel played sequentially, for which the outcomes have the following payoffs. What are the optimal strategies for this game? 
$\begin{array}{rr}
\text {Sole survivor }&\text { 2 point }\
\text {One of two survivors }&\text { 4 point }\
\text {One of three survivors}&\text { 3 point }\
\text {Nonsurvivor}&\text { 1 point }\
\end{array}$

Accepted Answer

First play

Question 18

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to column player II.   Does this game have a saddlepoint? What is each player's minimax or maximin strategy? Justify your response.

Accepted Answer

It has a saddlepoint

Question 19

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to column player II. 
$\left[ \begin{array} { c c c } 
2 & 3 & 4 \
5 & 6 & 7 \
8 & 9 & 10
\end{array} \right]$ 
Which of the following statements is true?

Accepted Answer

A)  The game has no saddlepoint. 
B)  There is a saddlepoint at row 1, column 1. 
C)  There is a saddlepoint at row 3, column 1. 
D)  There is a saddlepoint at row 3, column 3. 
A)  The game has no saddlepoint. 
B)  There is a saddlepoint at row 1, column 1. 
C)  There is a saddlepoint at row 3, column 1. 
D)  There is a saddlepoint at row 3, column 3.

Question 20

In the following game of batter-versus-pitcher in baseball, the batter's batting averages are shown in the game matrix.   Which of the following statements is true?

Accepted Answer

A)  The game has no saddlepoint. 
B)  The game has a saddlepoint; the value of the game is .200. 
C)  The game has a saddlepoint; the value of the game is .300. 
D)  The game has a saddlepoint; the value of the game is .400. 
A)  The game has no saddlepoint. 
B)  The game has a saddlepoint; the value of the game is .200. 
C)  The game has a saddlepoint; the value of the game is .300. 
D)  The game has a saddlepoint; the value of the game is .400.

Exam 15: Game Theory: the Mathematics of Competition

For a truel where the choices are sequential, which statement is true?

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to the column player II. [5221]\left[ \begin{array} { l l } 5 & 2 \\2 & 1\end{array} \right][52​21​] Which of the following statements is true?

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to the column player II. Which of the following statements is true? [5221]\left[ \begin{array} { l l } 5 & 2 \\2 & 1\end{array} \right][52​21​]

Construct the game tree for a truel played sequentially, for which the outcomes have the following payoffs. What are the optimal strategies for this game? Sole survivor 4 point One of two survivors 3 point One of three survivors 2 point Nonsurvivor 1 point

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to column player II. The maximin strategy of player I is:

Create a three-by-three matrix that represents a two-person zero-sum game in which each player has three options and at least one player has a dominated strategy.

For a truel where the choices are sequential, which statement is true?

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to column player II. The minimax strategy of player II is:

The game of Prisoner's Dilemma is an example of: I: a variable-sum game. II: a partial-conflict game.

Create a three-by-three matrix that represents a two-person zero-sum game in which each player has three options and the game has no saddlepoint.

Consider the following partial-conflict game played in a noncooperative manner. Which of the following statements is true?

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to column player II. Does this game have a saddlepoint? What is each player's minimax or maximin strategy? Justify your response.

Consider the following partial-conflict game played in a noncooperative manner. The first payoff is to player I; the second is to player II. Player II Player I Choice A Choice B Choice A (1,1) (2,6) Choice B (6,2) (5,5) What outcomes constitute a Nash equilibrium?

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to column player II. Does this game have a saddlepoint? What is each player's minimax or maximin strategy? Justify your response.

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to column player II. 3 7 2 1 4 6 9 5 8 Which of the following statements is true?

Construct the game tree for a truel played sequentially, for which the outcomes have the following payoffs. What are the optimal strategies for this game? Sole survivor 2 point One of two survivors 4 point One of three survivors 3 point Nonsurvivor 1 point

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to column player II. Does this game have a saddlepoint? What is each player's minimax or maximin strategy? Justify your response.

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to column player II. [2345678910]\left[ \begin{array} { c c c } 2 & 3 & 4 \\5 & 6 & 7 \\8 & 9 & 10\end{array} \right]​258​369​4710​​ Which of the following statements is true?

In the following game of batter-versus-pitcher in baseball, the batter's batting averages are shown in the game matrix. Which of the following statements is true?

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In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to the column player II. $\left[ \begin{array} { l l } 5 & 2 \\2 & 1\end{array} \right]$ Which of the following statements is true?

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to the column player II. Which of the following statements is true? $\left[ \begin{array} { l l } 5 & 2 \\2 & 1\end{array} \right]$

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to column player II. $\left[ \begin{array} { c c c } 2 & 3 & 4 \\5 & 6 & 7 \\8 & 9 & 10\end{array} \right]$ Which of the following statements is true?