Question 1

-Consider the static oil-drilling game depicted in Figure 16.2. The Nash equilibrium strategy profile for this game is:

Accepted Answer

A)  {Narrow, Narrow} 
B)  {Narrow 6 Narrow} 
C)  {Wide, Wide} 
D)  {Wide 6 Wide} 
E)  None of the above. 
A)  {Narrow, Narrow} 
B)  {Narrow 6 Narrow} 
C)  {Wide, Wide} 
D)  {Wide 6 Wide} 
E)  None of the above. C

Question 2

-Consider the Oil Drilling Game depicted in Figure 16.5. PETROX must decide whether to purchase a lease to drill for oil. Based on preliminary surveys, PETROX knows that there is an 80 percent chance that there is no oil (NO) and a 20 percent probability that oil is present (O). PETROX decides to conduct seismic surveys. The probability that the survey is negative when oil is present is P(!*O) = 0.5. The probability that there the survey is positive when no oil is present is P(+*NO) = 0.5. Payoffs are in millions of dollars. What is the probability that PETROX will strike oil when the seismic surveys indicate that oil is present?

Accepted Answer

A)  10 percent 
B)  20 percent 
C)  30 percent 
D)  40 percent 
E)  50 percent 
A)  10 percent 
B)  20 percent 
C)  30 percent 
D)  40 percent 
E)  50 percent B

Question 3

An improper subgame:

Accepted Answer

A)  Occurs when a subroot is located in an invalid information set. 
B)  Occurs when a subroot is located in a valid information set. 
C)  Assumes that the players do not have perfect recall. 
D)  Assumes that the players have total recall. 
E)  None of the above are correct. 
A)  Occurs when a subroot is located in an invalid information set. 
B)  Occurs when a subroot is located in a valid information set. 
C)  Assumes that the players do not have perfect recall. 
D)  Assumes that the players have total recall. 
E)  None of the above are correct. B

Question 4

-Consider the Spence Education Game depicted in Figure 16.4. In the figure, all payoffs are in thousands of dollars per month. Suppose that 30 percent of all workers are low- productivity (LP) workers and 70 percent are high-productivity (HP) workers. Using pre- employment testing, the firm has determined that there is a 60 percent probability of hiring a high-school (HS) graduate who is also a high-productivity worker and a 75 percent probability of hiring a college (C) graduate who is a high-productivity worker. What is the probability that the firm will hire a low-productivity, high school graduate?

Accepted Answer

A)  22 percent 
B)  44 percent 
C)  48 percent 
D)  52 percent 
E)  None of the above. 
A)  22 percent 
B)  44 percent 
C)  48 percent 
D)  52 percent 
E)  None of the above.

Question 5

-Consider the Oil Drilling Game depicted in Figure 16.5. PETROX must decide whether to purchase a lease to drill for oil. Based on preliminary surveys, PETROX knows that there is an 80 percent chance that there is no oil (NO) and a 20 percent probability that oil is present (O). PETROX decides to conduct seismic surveys. The probability that the survey is negative when oil is present is P(!*O) = 0.5. The probability that there the survey is positive when no oil is present is P(+*NO) = 0.5. Payoffs are in millions of dollars. What is PETROX's conditional expected payoff from drilling?

Accepted Answer

A)  $12 million 
B)  $8 million 
C)  !$22 million 
D)  !$38 million 
E)  !$42 million 
A)  $12 million 
B)  $8 million 
C)  !$22 million 
D)  !$38 million 
E)  !$42 million

Question 6

An invalid information set:

Accepted Answer

A)  Is a collection of decision nodes for two or more players. 
B)  A decision node where no decision node precedes any other. 
C)  A collection of information sets. 
D)  Is when the move by one player precedes the move by another player in the same information set. 
E)  Answers a and d are correct. 
A)  Is a collection of decision nodes for two or more players. 
B)  A decision node where no decision node precedes any other. 
C)  A collection of information sets. 
D)  Is when the move by one player precedes the move by another player in the same information set. 
E)  Answers a and d are correct.

Question 7

-Consider the Spence Education Game depicted in Figure 16.3. In the figure, all payoffs are in thousands of dollars per month. Suppose that 70 percent of all workers are low- productivity (LP) workers and 30 percent are high-productivity (HP) workers. Using pre- employment testing, the firm has determined that there is a 60 percent probability of hiring a high-school (HS) graduate who is also a high-productivity worker and a 75 percent probability of hiring a college (C) graduate who is a high-productivity worker. What is the firm's conditional expected payoff from hiring a college graduate?

Accepted Answer

A)  About $1,560 
B)  About $1,960 
C)  About $2,810 
D)  About $3,100 
E)  None of the above. 
A)  About $1,560 
B)  About $1,960 
C)  About $2,810 
D)  About $3,100 
E)  None of the above.

Question 8

-Consider the Spence Education Game depicted in Figure 16.4. In the figure, all payoffs are in thousands of dollars per month. Suppose that 30 percent of workers are low- productivity (LP) workers and 70 percent are high-productivity (HP) workers. Using pre- employment testing, the firm has determined that there is a 60 percent probability of hiring a high-school (HS) graduate who is also a high-productivity worker and a 75 percent probability of hiring a college (C) graduate who is a high-productivity worker. What is the firm's conditional expected payoff from hiring a high school graduate?

Accepted Answer

A)  About $2,000 
B)  About $2,480 
C)  About $3,250 
D)  About $3,560 
E)  About $4,000. 
A)  About $2,000 
B)  About $2,480 
C)  About $3,250 
D)  About $3,560 
E)  About $4,000.

Question 9

-Consider the Spence Education Game depicted in Figure 16.4. In the figure, all payoffs are in thousands of dollars per month. Suppose that 30 percent of workers are low- productivity (LP) workers and 70 percent are high-productivity (HP) workers. Using pre- employment testing, the firm has determined that there is a 60 percent probability of hiring a high-school (HS) graduate who is also a high-productivity worker and a 75 percent probability of hiring a college (C) graduate who is a high-productivity worker. What is the probability that the firm will hire a low-productivity worker who is a college graduate?

Accepted Answer

A)  28 percent 
B)  24 percent 
C)  12 percent 
D)  8 percent 
E)  None of the above. 
A)  28 percent 
B)  24 percent 
C)  12 percent 
D)  8 percent 
E)  None of the above.

Question 10

-Consider the Spence Education Game depicted in Figure 16.4. In the figure, all payoffs are in thousands of dollars per month. Suppose there is a 30 percent of workers are low- productivity (LP) workers and 70 percent are high-productivity (HP) workers. Using pre- employment testing, the firm decides to adopt a separating strategy by assuming that only high-productivity workers go to college and that workers who have only graduated high school are low-productivity types. What is the firm's conditional expected payoff from hiring a college graduate?

Accepted Answer

A)  $4,000 
B)  $3,500 
C)  $4,450 
D)  $5,760 
E)  $6,000 
A)  $4,000 
B)  $3,500 
C)  $4,450 
D)  $5,760 
E)  $6,000

Question 11

In dynamic games with imperfect information:

Accepted Answer

A)  Players are unaware of there position in the game tree because they move simultaneously. 
B)  Players have private information. 
C)  Players have incomplete information. 
D)  Answers b and c are correct. 
E)  All of the above. 
A)  Players are unaware of there position in the game tree because they move simultaneously. 
B)  Players have private information. 
C)  Players have incomplete information. 
D)  Answers b and c are correct. 
E)  All of the above.

Question 12

Total recall:

Accepted Answer

A)  Is typical of one-time, static games with incomplete information. 
B)  Is typical of one-time, static games with complete information. 
C)  Is characteristic of valid information sets. 
D)  Is characteristic of dynamic games with complete information. 
E)  Answers c and d are correct. 
A)  Is typical of one-time, static games with incomplete information. 
B)  Is typical of one-time, static games with complete information. 
C)  Is characteristic of valid information sets. 
D)  Is characteristic of dynamic games with complete information. 
E)  Answers c and d are correct.

Question 13

-Consider the Spence Education Game depicted in Figure 16.3. In the figure, all payoffs are in thousands of dollars per month. Suppose that 70 percent of all workers are low- productivity (LP) workers and 30 percent are high-productivity (HP) workers. Using pre- employment testing, the firm has determined that there is a 60 percent probability of hiring a high-school (HS) graduate who is also a high-productivity worker and a 75 percent probability of hiring a college (C) graduate who is a high-productivity worker. What is the probability that the firm will hire a low-productivity worker who is a high school graduate?

Accepted Answer

A)  44 percent 
B)  53 percent 
C)  61 percent 
D)  77 percent 
E)  None of the above. 
A)  44 percent 
B)  53 percent 
C)  61 percent 
D)  77 percent 
E)  None of the above.

Question 14

-Consider the Oil Drilling Game depicted in Figure 16.5. PETROX must decide whether to purchase a lease to drill for oil. Based on preliminary surveys, PETROX knows that there is an 80 percent chance that there is no oil (NO) and a 20 percent probability that oil is present (O). PETROX decides to conduct seismic surveys. The probability that the survey is negative when oil is present is P(!*O) = 0.5. The probability that there the survey is positive when no oil is present is P(+*NO) = 0.5. Payoffs are in millions of dollars. What is the probability that PETROX will not strike oil when the seismic surveys indicate that oil is present?

Accepted Answer

A)  40 percent 
B)  50 percent 
C)  60 percent 
D)  80 percent 
E)  90 percent 
A)  40 percent 
B)  50 percent 
C)  60 percent 
D)  80 percent 
E)  90 percent

Question 15

-Consider the static oil-drilling game depicted in Figure 16.2. The decision nodes D2 and D3 are collectively referred to as:

Accepted Answer

A)  An invalid information set. 
B)  A valid information set. 
C)  An information partition. 
D)  Improper subgame. 
E)  Belief profile. 
A)  An invalid information set. 
B)  A valid information set. 
C)  An information partition. 
D)  Improper subgame. 
E)  Belief profile.

Question 16

-Consider the Spence Education Game depicted in Figure 16.3. In the figure, all payoffs are in thousands of dollars per month. Suppose that 70 percent of all workers are low- productivity (LP) workers and 30 percent are high-productivity (HP) workers. Using pre- employment testing, the firm has determined that there is a 60 percent probability of hiring a high-school (HS) graduate who is also a high-productivity worker and a 75 percent probability of hiring a college (C) graduate who is a high-productivity worker. What is the probability that the firm will hire a high-productivity worker who is a college graduate?

Accepted Answer

A)  23 percent 
B)  39 percent 
C)  47 percent 
D)  56 percent 
E)  None of the above. 
A)  23 percent 
B)  39 percent 
C)  47 percent 
D)  56 percent 
E)  None of the above.

Question 17

-Consider the Spence Education Game depicted in Figure 16.4. In the figure, all payoffs are in thousands of dollars per month. Suppose that 30 percent of all workers are low- productivity (LP) workers and 70 percent are high-productivity (HP) workers. Using pre- employment testing, the firm has determined that there is a 60 percent probability of hiring a high-school (HS) graduate who is also a high-productivity worker and a 75 percent probability of hiring a college (C) graduate who is a high-productivity worker. What is the probability that the firm will hire a high-productivity worker who is a high school graduate?

Accepted Answer

A)  48 percent 
B)  52 percent 
C)  56 percent 
D)  78 percent 
E)  None of the above. 
A)  48 percent 
B)  52 percent 
C)  56 percent 
D)  78 percent 
E)  None of the above.

Question 18

-Consider the Spence Education Game depicted in Figure 16.3. In the figure, all payoffs are in thousands of dollars per month. Suppose that 70 percent of all workers are low- productivity (LP) workers and 30 percent are high-productivity (HP) workers. Using pre- employment testing, the firm has determined that there is a 60 percent probability of hiring a high-school (HS) graduate who is also a high-productivity worker and a 75 percent probability of hiring a college (C) graduate who is a high-productivity worker. What is the probability that the firm will hire a low-productivity worker who is a college graduate?

Accepted Answer

A)  44 percent 
B)  53 percent 
C)  61 percent 
D)  77 percent 
E)  None of the above. 
A)  44 percent 
B)  53 percent 
C)  61 percent 
D)  77 percent 
E)  None of the above.

Question 19

-Consider the Spence Education Game depicted in Figure 16.3. In the figure, all payoffs are in thousands of dollars per month. Suppose that 70 percent of all workers are low- productivity (LP) workers and 30 percent are high-productivity (HP) workers. Using pre- employment testing, the firm has determined that there is a 60 percent probability of hiring a high-school (HS) graduate who is also a high-productivity worker and a 75 percent probability of hiring a college (C) graduate who is a high-productivity worker. What is the optimal hiring strategy of a risk-neutral firm?

Accepted Answer

A)  Hire only college graduates. 
B)  Hire college graduates 75 percent of the time. 
C)  Hire only high-school graduates. 
D)  Hire high-school graduates 60 percent of the time. 
E)  Hire high-school and college graduates 50 percent. 
A)  Hire only college graduates. 
B)  Hire college graduates 75 percent of the time. 
C)  Hire only high-school graduates. 
D)  Hire high-school graduates 60 percent of the time. 
E)  Hire high-school and college graduates 50 percent.

Question 20

-Consider the Spence Education Game depicted in Figure 16.3. In the figure, all payoffs are in thousands of dollars per month. Suppose that 70 percent of all workers are low- productivity (LP) workers and 30 percent are high-productivity (HP) workers. Using pre- employment testing, the firm decides to adopt a separating strategy by assuming that only high-productivity workers go to college and that workers who have only graduated high school are low-productivity types. What is the firm's conditional expected payoff from hiring a college graduate?

Accepted Answer

A)  $5,000 
B)  $3,500 
C)  $2,810 
D)  $1,960 
E)  $1,560 
A)  $5,000 
B)  $3,500 
C)  $2,810 
D)  $1,960 
E)  $1,560

-Consider the static oil-drilling game depicted in Figure 16.2. The Nash equilibrium strategy profile for this game is:

An improper subgame:

An invalid information set:

In dynamic games with imperfect information:

Total recall:

-Consider the static oil-drilling game depicted in Figure 16.2. The decision nodes D₂ and D₃ are collectively referred to as:

Introduction to Game Theory

Noncooperative, One-Time, Static Games

Focal-Point and Evolutionary Equilibria

Infinitely-Repeated, Static Games

Finitely-Repeated, Static Games

Mixing Pure Strategies

Static Games With Continuous Strategies

Imperfect Competition

Perfect Competition and Monopoly

Strategic Trade Policy

Dynamic Games With Complete

Bargaining

Pure Strategies With Uncertain Payoffs

Torts and Contracts

Auctions

Filters

Exam 16: Dynamic Games With Incomplete Information

-Consider the static oil-drilling game depicted in Figure 16.2. The Nash equilibrium strategy profile for this game is:

An improper subgame:

An invalid information set:

In dynamic games with imperfect information:

Total recall:

-Consider the static oil-drilling game depicted in Figure 16.2. The decision nodes D2 and D3 are collectively referred to as:

Introduction to Game Theory

Noncooperative, One-Time, Static Games

Focal-Point and Evolutionary Equilibria

Infinitely-Repeated, Static Games

Finitely-Repeated, Static Games

Mixing Pure Strategies

Static Games With Continuous Strategies

Imperfect Competition

Perfect Competition and Monopoly

Strategic Trade Policy

Dynamic Games With Complete

Bargaining

Pure Strategies With Uncertain Payoffs

Torts and Contracts

Auctions

Filters

-Consider the static oil-drilling game depicted in Figure 16.2. The decision nodes D₂ and D₃ are collectively referred to as: