Question 1

Consider the following partial-conflict game played in a noncooperative manner. The first payoff is to player I; the second is to player II. $\begin{array}{lcc} 
& {\text { Player II }} \
\text { Player I } & \text { Choice A } & \text { Choice B } \
\text { Choice A } & (1,9) & (3,3) \
\text { Choice B } & (5,5) & (9,1)
\end{array}$
Discuss the players' possible strategies when this game is played.

Accepted Answer

The answer of Consider the following partial-conflict game played in...

Question 2

In the following game of batter-versus-pitcher in baseball, the batter's batting averages are shown in the game matrix.  What is the pitcher's optimal strategy?

Accepted Answer

A)  Pitch more fastballs than curves. 
B)  Pitch more curves than fastballs. 
C)  Pitch fastballs and curves equally.

Question 3

Which of the following is not correct for the game of Chicken?

Accepted Answer

A)  It is a two-person variable sum game. 
B)  Each player has two strategies: to swerve to avoid a collision or not to swerve. 
C)  Neither player has a dominant strategy. 
D)  There is no Nash equilibrium.

Question 4

Use the following information to answer the Questions:
In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to the column player II. $$\left[ \begin{array} { c c c c } 
- 3 & 4 & 1 & 2 \
6 & - 1 & 2 & 1 \
3 & 2 & 3 & 6 \
1 & - 4 & 2 & 5
\end{array} \right]$$
-Does the game have a saddlepoint?

Accepted Answer

A) True 
 B)False

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. 
$\left| \begin{array} { l l } 
4 & 2 \
9 & 6
\end{array} \right|$ 
Does this game have a saddlepoint? What is each player's minimax or maximin strategy? Justify your response.

Accepted Answer

The answer of In the following two-person zero-sum game, the...

Question 6

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to the column player II. $$\left[ \begin{array} { l l l l } 
8 & 1 & 5 & 2 \
5 & 4 & 7 & 8 \
1 & 3 & 4 & 5 \
8 & 4 & 3 & 5
\end{array} \right]$$ 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 2. 
C)  The game has a saddlepoint; the value of the game is 3. 
D)  The game has a saddlepoint; the value of the game is 4.

Question 7

Describe a Nash equilibrium.

Accepted Answer

The answer of Describe a Nash equilibrium....

Question 8

In the game of matching pennies, player I wins a penny if the coins match and player II wins if the coins do not match. Present this game as a two-by-two matrix, where each player has two outcomes from which to select.

Accepted Answer

The answer of In the game of matching pennies, player...

Question 9

Use the following information to answer the Questions:

-Which of the following statements is true?

Accepted Answer

A)  Both player I and player II have dominant strategies. 
B)  Neither player I nor II has a dominant strategy. 
C)  Only player I has a dominant strategy. 
D)  Only player II has a dominant strategy.

Question 10

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.

Question 11

Use the following information to answer the Questions:
In American football the "third down and short" situation occurs often. The probabilities of obtaining a first down, shown below, are dependent on the choice of the offense and the anticipated choice of the defense. $\begin{array}{lll}
&&&\text { Defense }\
&&\text { Run } &&\text { Pass }\
\text { Offense }&\text { Run } & 0.2 && 0.8 \
&\text { Pass } & 0.5 && 0.1
\end{array}$
-Suppose the value of the game is $p$ What does this mean for the offense?

Accepted Answer

The answer of Use the following information to answer the...

Question 12

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to the column player II. 
$\left[ \begin{array} { l l l } 
5 & 8 & 6 \
4 & 3 & 1 \
2 & 6 & 7
\end{array} \right]$ 
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.

Question 13

Use the following information to answer the Questions:
In American football the "third down and short" situation occurs often. The probabilities of obtaining a first down, shown below, are dependent on the choice of the offense and the anticipated choice of the defense. $\begin{array}{lll}
&&&\text { Defense }\
&&\text { Run } &&\text { Pass }\
\text { Offense }&\text { Run } & 0.2 && 0.8 \
&\text { Pass } & 0.5 && 0.1
\end{array}$
-What is the optimal mixed strategy for the offense?

Accepted Answer

The answer of Use the following information to answer the...

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.  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.

Question 15

The game of Chicken 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

Question 16

Suppose on a committee of three people Kim (the chair), Chris, and Terry each have one vote, but Kim breaks any tie. In attempting to elect someone to drive the van, each person has a priority list: $\begin{array}{clll}
&\mid& \text { Kim's Priorities}&\text { Chris's Priorities}&\text { Terry's Priorities}\
\hline \text { 1st choice } &\mid&\text { Chris } & \text { Kim } & \text { Terry } \
\text { 2nd choice }&\mid &\text { Kim } & \text { Chris } & \text { Chris } \
\text { 3rd choice } &\mid& \text { Terry } & \text { Terry } & \text { Kim }
\end{array}$ Which of the following are Nash equilibria? 
I: Every person votes for his/her first choice.
II: Kim and Chris vote for Chris; Terry votes for Terry.

Accepted Answer

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

Question 17

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to the column player II. 
$\left[ \begin{array} { l l l } 
5 & 8 & 6 \
4 & 3 & 1 \
2 & 6 & 7
\end{array} \right]$
 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.

Question 18

Use the following information to answer Questions The probabilities of obtaining a first down, shown below, are dependent on the choice of the offense and the anticipated choice of the defense. $\begin{array}{lll}
&&&\text { Defense }\
&&\text { Run } &&\text { Pass }\
\text { Offense }&\text { Run } & 0.5 && 0.6 \
&\text { Pass } & 0.8 && 0.4
\end{array}$
-In such situations, what is the optimal solution for the defense?

Accepted Answer

A)  always anticipate a run 
B)  always anticipate a pass 
C)  play the mixed strategy $\left( \frac { 2 } { 5 } , \frac { 3 } { 5 } \right)$ 
D)  play the mixed strategy $\left( \frac { 4 } { 5 } , \frac { 1 } { 5 } \right)$

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. 
$\left[ \begin{array} { c c } 
1 & - 2 \
- 2 & 1
\end{array} \right]$ 
Which of the following statements is true?

Accepted Answer

A)  The game has no saddlepoint. 
B)  There is a saddlepoint at row 2, column 2. 
C)  There is a saddlepoint at row 2, column 1. 
D)  There is a saddlepoint at row 1, column 2.

Question 20

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to column player II.  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 8. 
C)  The game has a saddlepoint; the value of the game is 9. 
D)  The game has a saddlepoint; the value of the game is 11.

Exam 15: Game Theory: the Mathematics of Competition

In the following game of batter-versus-pitcher in baseball, the batter's batting averages are shown in the game matrix. What is the pitcher's optimal strategy?

Which of the following is not correct for the game of Chicken?

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

Describe a Nash equilibrium.

In the game of matching pennies, player I wins a penny if the coins match and player II wins if the coins do not match. Present this game as a two-by-two matrix, where each player has two outcomes from which to select.

Use the following information to answer the Questions: -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. The maximin strategy of player I is:

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to the column player II. $\left[ \begin{array} { l l l } 5 & 8 & 6 \\4 & 3 & 1 \\2 & 6 & 7\end{array} \right]$ The minimax strategy of player II is:

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 Chicken is an example of: I: a variable-sum game. II: a partial-conflict game.

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to the column player II. $\left[ \begin{array} { l l l } 5 & 8 & 6 \\4 & 3 & 1 \\2 & 6 & 7\end{array} \right]$ The maximin strategy of player I is:

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

Exam 15: Game Theory: the Mathematics of Competition

In the following game of batter-versus-pitcher in baseball, the batter's batting averages are shown in the game matrix. What is the pitcher's optimal strategy?

Which of the following is not correct for the game of Chicken?

Describe a Nash equilibrium.

In the game of matching pennies, player I wins a penny if the coins match and player II wins if the coins do not match. Present this game as a two-by-two matrix, where each player has two outcomes from which to select.

Use the following information to answer the Questions: -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. The maximin strategy of player I is:

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to the column player II. [586431267]\left[ \begin{array} { l l l } 5 & 8 & 6 \\4 & 3 & 1 \\2 & 6 & 7\end{array} \right]​542​836​617​​ The minimax strategy of player II is:

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 Chicken is an example of: I: a variable-sum game. II: a partial-conflict game.

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to the column player II. [586431267]\left[ \begin{array} { l l l } 5 & 8 & 6 \\4 & 3 & 1 \\2 & 6 & 7\end{array} \right]​542​836​617​​ The maximin strategy of player I is:

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to column player II. [1−2−21]\left[ \begin{array} { c c } 1 & - 2 \\- 2 & 1\end{array} \right][1−2​−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 column player II. 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. $\left[ \begin{array} { l l l } 5 & 8 & 6 \\4 & 3 & 1 \\2 & 6 & 7\end{array} \right]$ The minimax strategy of player II is:

In the following two-person zero-sum game, the payoffs represent gains to the row player I and losses to the column player II. $\left[ \begin{array} { l l l } 5 & 8 & 6 \\4 & 3 & 1 \\2 & 6 & 7\end{array} \right]$ The maximin strategy of player I is:

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