1.	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?	
A)	The game has no saddle point.	
B)	The game has a saddle point; the value of the game is 3.	
C)	The game has a saddle point; the value of the game is 2.	
D)	The game has a saddle point; the value of the game is 2.5.	

2.	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?	
A)	The game has no saddle point.	
B)	The game has a saddle point; the value of the game is 3.	
C)	The game has a saddle point; the value of the game is 4.	
D)	The game has a saddle point; the value of the game is 3.5.	

3.	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?	
A)	The game has no saddle point.	
B)	The game has a saddle point; the value of the game is 3.	
C)	The game has a saddle point; the value of the game is 4.	
D)	The game has a saddle point; the value of the game is 5.	

4.	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?	
A)	The game has no saddle point.	
B)	The game has a saddle point; the value of the game is 2.	
C)	The game has a saddle point; the value of the game is 5.	
D)	The game has a saddle point; the value of the game is 6.	

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

6.	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?	
A)	The game has no saddle point.	
B)	The game has a saddle point; the value of the game is 8.	
C)	The game has a saddle point; the value of the game is 9.	
D)	The game has a saddle point; the value of the game is 11.	

7.	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?	
A)	The game has no saddle point.	
B)	The game has a saddle point; the value of the game is 8.	
C)	The game has a saddle point; the value of the game is 9.	
D)	The game has a saddle point; the value of the game is 11.	

8.	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?	
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.	

9.	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?	
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.	

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

11.	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	
A)	to always play the first column.	C)	to always play the third column.	
B)	to always play the second column.	D)	to play two or more of the columns.	

12.	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	
A)	to always play the first row.	C)	to always play the third row.	
B)	to always play the second row.	D)	to play two or more of the rows.	

13.	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	
A)	to always play the first column.	C)	to always play the third column.	
B)	to always play the second column.	D)	to play two or more of the columns.	

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 maximin strategy of Player I is	
A)	to always play the first row.	C)	to always play the third row.	
B)	to always play the second row.	D)	to play two or more of the rows.	

15.	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	
A)	to always play the first column.	C)	to always play the third column.	
B)	to always play the second column.	D)	to play two or more of the columns.	

16.	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	
A)	to always play the first row.	C)	to always play the third row.	
B)	to always play the second row.	D)	to always play the fourth row.	

17.	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	
A)	to always play the first column.	C)	to always play the third column.	
B)	to always play the second column.	D)	to always play the fourth column.	

18.	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	
A)	to always play the first row.	C)	to always play the third row.	
B)	to always play the second row.	D)	to always play the fourth row.	

19.	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	
A)	to always play the first column.	C)	to always play the third column.	
B)	to always play the second column.	D)	to always play the fourth column.	

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

21.	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?	
A)	The game has no saddle point.	
B)	The game has a saddle point; the value of the game is .200.	
C)	The game has a saddle point; the value of the game is .300.	
D)	The game has a saddle point; the value of the game is .400.	

22.	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?	
A)	Pitch more fastballs than curves.	C)	Pitch fastballs and curves equally.	
B)	Pitch more curves than fastballs.			

23.	In the following game of batter-versus-pitcher in baseball, the batter's batting averages are shown in the game matrix.

 
What is the batter's optimal strategy?	
A)	Expect more fastballs than curves.	
B)	Expect more curves than fastballs.	
C)	Expect equal numbers of curves and fastballs.	

24.	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?	
A)	Pitch more fastballs than curves.	C)	Pitch fastballs and curves equally.	
B)	Pitch more curves than fastballs.			

25.	In the following game of batter-versus-pitcher in baseball, the batter's batting averages are shown in the game matrix.

 
What is the batter's optimal strategy?	
A)	Expect more fastballs than curves.	
B)	Expect more curves than fastballs.	
C)	Expect equal numbers of curves and fastballs.	

26.	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?	
A)	This game has no saddle point.	
B)	This game has a saddle point; the value of the game is $100.	
C)	This game has a saddle point; the value of the game is $200.	
D)	This game has a saddle point; the value of the game is $500.	

27.	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 pay 50% of any repair bill: that is, you will pay either $50 or $250 for the subsequent repair.  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?	
A)	This game has no saddle point.	
B)	This game has a saddle point; the value of the game is $200.	
C)	This game has a saddle point; the value of the game is $250.	
D)	This game has a saddle point; the value of the game is $450.	

28.	As the buyer for your business, you can choose to buy an extended warranty for each new computer for $200 each.  During this period, each computer will experience either a minor ($100) or major ($500) repair bill.  Repairs for each warranted computer are reduced by 50% to $50 or $250.  Assume the computer company wants to make as much money as possible, and you wish to spend as little as possible. 
 
What is your optimal strategy?	
A)	Never buy the warranty.	
B)	Always buy the warranty.	
C)	Buy the warranty for less than half of the computers.	
D)	Buy the warranty for more than half of the computers.	

29.	As the buyer for your business, you can choose to buy an extended warranty for each new computer for $200 each.  During this period, each computer will experience either a minor ($100) or major ($500) repair bill.  Repairs for each warranted computer are reduced by 50% to $50 or $250.  Assume the computer company wants to make as much money as possible, and you wish to spend as little as possible. 
 
What is the computer company's optimal strategy?	
A)	Always sell the warranty.	
B)	Never sell the warranty.	
C)	Sell the warranty for less than half of the computers.	
D)	Sell the warranty for more than half of the computers.	

30.	You are considering cheating on your income tax return.  If you cheat you will pay $1000 in taxes; if you don't cheat you will pay $2000.  If you are audited and you didn't cheat, your auditor will be kind and reduce your taxes from $2000 to $1500.  If you are audited and you did cheat, you will be caught and have to pay a total of $2500, including penalties.
 
Statistically, which is the best option for you to choose?	
A)	Definitely cheat.	C)	Probably don't cheat.	
B)	Probably cheat.	D)	Definitely don't cheat.	

31.	If you cheat on your income tax return you will pay $1000 in taxes; if you don't cheat you will pay $2000.  If you are audited and you didn't cheat, your auditor will be kind and reduce your taxes from $2000 to $1500.  If you are audited and you did cheat, you will be caught and have to pay a total of $2500, including penalties.
 
Assuming the government wants to receive as much money as possible, statistically, which is the best option for the government to choose?	
	A)  Always audit.    B)  Usually audit.    C)  Occasionally audit.    D)  Never audit.	

32.	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.

 
In such situations, what is the optimal solution for the defense?	
A)	Always anticipate a run.	
B)	Always anticipate a pass.	
C)	Anticipate a run more often than a pass.	
D)	Anticipate a pass more often than a run.	

33.	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.

 
In such situations, what is the optimal solution for the offense?	
A)	Always choose to run.	C)	Choose to run more often than pass.	
B)	Always choose to pass.	D)	Choose to pass more often than run.	

34.	Consider the following partial-conflict game played in a non-cooperative manner.

 
What outcomes constitute a Nash equilibrium?	
A)	Only when both players select choice A.	
B)	Only when both players select choice B.	
C)	Only when one player selects choice A; the other selects choice B.	
D)	Only when both players select choice A or both players select choice B.	

35.	Consider the following partial-conflict game played in a non-cooperative manner.

 
Which of the following statements is true?	
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.	

36.	Consider the following partial-conflict game played in a non-cooperative manner.

 
Which of the following statements is true?	
A)	Both Player I and Player II have a dominant strategy.	
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.	

37.	Consider the following partial-conflict game played in a non-cooperative manner.

 
Which of the following is a Nash equilibrium?	
A)	Player I selects choice A; Player II selects choice A.	
B)	Player I selects choice A; Player II selects choice B.	
C)	Player I selects choice B; Player II selects choice A.	
D)	Player I selects choice B; Player II selects choice B.	

38.	Consider the following partial-conflict game played in a non-cooperative manner.

 
Assume that the game is played continually, and players can change their choices at noon each day.  If the game begins with both players selecting Choice B, what should happen at the first opportunity to change?	
A)	Nothing.	C)	Player II switches to choice A.	
B)	Player I switches to choice A.	D)	Both players switch to choice A.	

39.	Consider the following partial-conflict game played in a non-cooperative manner.

 
Assume that the game is played continually, and players can change their choices at noon each day.  If the game begins with both players selecting choice A, what should happen at the first opportunity to change?	
A)	Nothing.	C)	Player II switches to choice B.	
B)	Player I switches to choice B.	D)	Both players switch to choice B.	

40.	Suppose on a committee of three people the chair, Chris, and Terry each have one vote; Kim breaks any tie.  In attempting to elect someone to host the summer picnic, each person has a priority list: 

 
Which of the following are Nash equilibria?

I:  Every person votes for his/her first choice.	

II: Every person votes for his/her second choice.	

	A)  I only    B)  II only    C)  Both I and II    D)  Neither I nor II	

41.	Suppose on a committee of three people the chair, Chris, and Terry each have one vote; Kim breaks any tie.  In attempting to elect someone to host the summer picnic, each person has a priority list: 

 
Which of the following are Nash equilibria?

I:  Every person votes for Kim.	

II: Every person votes for Chris.	

	A)  I only    B)  II only    C)  Both I and II    D)  Neither I nor II	

42.	Suppose on a committee of three people the chair, Chris, and Terry each have one vote; Kim breaks any tie.  In attempting to elect someone to drive the van, each person has a priority list: 

 
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.	

	A)  I only    B)  II only    C)  Both I and II    D)  Neither I nor II	

43.	Suppose on a committee of three people the chair, Chris, and Terry each have one vote; Kim breaks any tie.  In attempting to elect someone to drive the van, each person has a priority list: 

 
Which of the following are Nash equilibria?

I:  Every person votes for Chris.	

II: Every person votes for his/her second choice.	

	A)  I only    B)  II only    C)  Both I and II    D)  Neither I nor II	

44.	The game of Chicken is an example of
 
I: a variable-sum game.
II: a partial-conflict game.	
	A)  I only    B)  II only    C)  Both I and II    D)  Neither I nor II	

45.	The game of Prisoner's Dilemma is an example of
 
I: a variable-sum game.
II: a partial-conflict game.	
	A)  I only    B)  II only    C)  Both I and II    D)  Neither I nor II	

46.	The "status-quo paradox"
 
I: doesn't really happen.
II: can allow a favored candidate to lose.	
	A)  I only    B)  II only    C)  Both I and II    D)  Neither I nor II	

47.	In a pure strategy game, each player consistently selects one particular option.	
	A)  True    B)  False	

48.	In a symmetrical game, both players will always choose the same particular option.	
	A)  True    B)  False	

49.	Every "zero-sum" game is a "fair" game.	
	A)  True    B)  False	

50.	Game theory is used by intelligence services to check for security violations.	
	A)  True    B)  False	

51.	In a truel where the choices are simultaneous, what is the optimal strategy for each player?	
	A)  fire at another player    B)  fire at himself    C)  do not fire	

52.	In a truel where the choices are sequential, what is the optimal strategy for the first player?	
	A)  fire at another player    B)  fire at himself    C)  do not fire	

53.	In a truel where the choices are simultaneous, what is the probability that any particular player will survive?	
	A)  0    B)  1/4    C)  1/3    D)  1	

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

55.	For a truel where the choices are sequential, which statement is true?	
A)	The game tree has no cut branches.	C)	The game tree has four cut branches.	
B)	The game tree has two cut branches.	D)	The game tree has six cut branches.	

56.	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?	
A)	The game has no saddle point.	
B)	The game has a saddle point; the value of the game is 1.	
C)	The game has a saddle point; the value of the game is 2.	
D)	The game has a saddle point; the value of the game is 5.	

57.	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?	
A)	The game has no saddle point.	
B)	The game has a saddle point; the value of the game is 5.	
C)	The game has a saddle point; the value of the game is 6.	
D)	The game has a saddle point; the value of the game is 8.	

58.	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?	
A)	The game has no saddle point.	
B)	The game has a saddle point; the value of the game is 2.	
C)	The game has a saddle point; the value of the game is 3.	
D)	The game has a saddle point; the value of the game is 4.	

59.	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?

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.	

60.	In the following two-person zero-sum game, the payoffs represent gains to the row Player I and losses to the column Player II. 

 
The maximin strategy of Player I is	
A)	to always play the first row.	C)	to always play the third row.	
B)	to always play the second row.	D)	to play two or more of the rows.	

61.	In the following two-person zero-sum game, the payoffs represent gains to the row Player I and losses to the column Player II. 

 
The minimax strategy of Player II is	
A)	to always play the first column.	C)	to always play the third column.	
B)	to always play the second column.	D)	to play two or more of the columns.	

62.	In the following two-person zero-sum game, the payoffs represent gains to the row Player I and losses to the column Player II. 

 
The maximin strategy of Player I is	
A)	to always play the first row.	C)	to always play the third row.	
B)	to always play the second row.	D)	to play two or more of the rows.	

63.	In the following two-person zero-sum game, the payoffs represent gains to the row Player I and losses to the column Player II. 

 
The minimax strategy of Player II is	
A)	to always play the first column.	C)	to always play the third column.	
B)	to always play the second column.	D)	to play two or more of the columns.	

64.	Consider the following partial-conflict game played in a non-cooperative 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?	
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	

65.	Consider the following partial-conflict game played in a non-cooperative manner. The first payoff is to Player I; the second is to Player II.

Player II	

Player I	
Choice A	
Choice B	

Choice A	
(2, 4)	
(3, 6)	

Choice B	
(6, 3)	
(4, 2)	

What outcomes constitute a Nash equilibrium?	
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	

Answer Key

1.	A	
2.	A	
3.	A	
4.	A	
5.	A	
6.	A	
7.	C	
8.	D	
9.	A	
10.	C	
11.	C	
12.	C	
13.	C	
14.	C	
15.	B	
16.	D	
17.	B	
18.	D	
19.	A	
20.	A	
21.	A	
22.	A	
23.	B	
24.	B	
25.	B	
26.	C	
27.	C	
28.	C	
29.	C	
30.	C	
31.	C	
32.	C	
33.	C	
34.	A	
35.	A	
36.	A	
37.	B	
38.	B	
39.	C	
40.	D	
41.	C	
42.	C	
43.	C	
44.	C	
45.	C	
46.	B	
47.	A	
48.	B	
49.	B	
50.	A	
51.	A	
52.	C	
53.	B	
54.	B	
55.	C	
56.	C	
57.	B	
58.	D	
59.	C	
60.	A	
61.	A	
62.	B	
63.	B	
64.	B	
65.	C