Deck 16: Dynamic Games With Incomplete Information

Question 1

In dynamic games with imperfect information:

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.

Answer 1

Answers b and c are correct.

Question 2

A player who cannot distinguish among decisions nodes at a stage of a dynamic games is:

A) Within an information partition.
B) Within an invalid information set.
C) Within a valid information set.
D) Is playing an improper subgame.
E) Answers c and d are correct.

Answer 2

Answers c and d are correct.

Question 3

An invalid information set:

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.

Answer 3

Answers a and d are correct.

Question 4

-Refer to Figure 16.1, which represents a static game in extensive format. The following decision nodes constitute a valid information set:

A) D₁ and D₂.
B) D₁ and D₃.
C) D₂ and D₃.
D) D₁, D₂, and D₃.
E) Answers a and b are correct.

Question 5

-Refer to Figure 16.1, which represents a static game in extensive format. The following decision nodes constitute an invalid information set:

A) D₁ and D₂.
B) D₁ and D₃.
C) D₂ and D₃.
D) D₁, D₂, and D₃.
E) Answers a and b are correct.

Question 6

-Refer to Figure 16.1, which represents a static game in extensive format. The Nash equilibrium strategy profile for this game is:

A) {Up, Up}.
B) {Down, Down}.
C) {Up, Down}.
D) {Down, Up}.

Question 7

An improper subgame:

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.

Question 8

Total recall:

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 9

Perfect recall:

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

Question 10

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

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

Question 11

-Consider the static oil-drilling game depicted in Figure 16.2. This game is an example of :

A) A multistage game.
B) A Harsanyi transformation.
C) Nash bargaining.
D) Prisoner's dilemma.
E) Screening.

Question 12

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

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

Question 13

-Consider the static oil-drilling game depicted in Figure 16.2. The payoffs to both players from Nash equilibrium strategy profile for this game are:

A) (52, 52).
B) (12, 70)
C) (70, 12)
D) (24, 24)
E) Cannot be determined without additional information about the players' positions in the game tree.

Question 14

-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 high school graduate?

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

Question 15

-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?

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

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?

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 16.3. 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?

A) 44 percent
B) 53 percent
C) 61 percent
D) 77 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 firm's conditional expected payoff from hiring a high school graduate?

A) About $1,560
B) About $1,960
C) About $2,810
D) About $3,100
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 firm's conditional expected payoff from hiring a college graduate?

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

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 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?

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 21

-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?

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

Question 22

-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?

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

Question 23

-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?

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

Question 24

-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 high-productivity, college graduate?

A) 72 percent
B) 76 percent
C) 88 percent
D) 92 percent
E) None of the above.

Question 25

-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?

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

Question 26

-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?

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

Question 27

-Consider the Spence Education Game depicted in Figure 16.4. In the figure, all payoffs are in thousands of dollars per month. Suppose 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 college graduate?

A) About $6,000
B) About $5,760
C) About $4,370
D) About $3,580
E) About $4,000.

Question 28

-Consider the Spence Education Game depicted in Figure 16.4. In the figure, all payoffs are in thousands of dollars per month. Suppose that Nature moves first and determines that there is a 30 percent of workers are low-productivity (LP) workers and 70 percent are high-productivity (HP) workers. 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?

A) Hire only college graduates.
B) Hire college graduates 70 percent of the time.
C) Hire only high-school graduates.
D) Hire high-school graduates 30 percent of the time.
E) Hire high-school graduates 50 percent of the time.

Question 29

-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?

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

Question 30

-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?

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

Question 31

-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?

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

Question 32

-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?

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

Question 33

Screening occurs when a player:

A) Transmits a credible and unreproducible signal to an uninformed player.
B) Attempts to sort rivals according to certain characteristics.
C) Attempts to sort rivals using different credible threats.
D) Attempts to obtain a better payoffs by committing to a different strategy for each rival.
E) Makes a decision using a familiar frame of reference.

Question 34

Self-selection occurs when players:

A) Transmit a credible and unreproducible signals to an uninformed rivals.
B) Have do not have total recall.
C) Move first to limit a rivals strategy options.
D) Have an incentive to cooperate with rivals of similar characteristics.
E) Voluntarily sort themselves into different groups have certain characteristics.