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.

Accepted Answer

In dynamic games with imperfect information, players have private information (which others do not know) and incomplete information (not knowing all the elements of the game structure, such as payoffs or strategies of other players), making both B and C 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.

Accepted Answer

E

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.

Accepted Answer

An invalid information set in game theory occurs when the information set includes scenarios where one player's move precedes another within the same set (D), or it involves decision nodes for two or more players (A), which contradicts the definition of an information set being a collection of points in a game where a player has the same information.

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.

Accepted Answer

In a static game in extensive format, a valid information set consists of decision nodes that are indistinguishable to the player making the decision. D₂ and D₃ can be part of the same information set if the player cannot distinguish between them based on the information available.

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.

Accepted Answer

An information set in game theory represents a situation where a player cannot distinguish between different game states due to a lack of information about previous moves. For an information set to be valid, all decision nodes within it must be reachable by the player under the same history of moves by all players. Choices A and B describe sets of decision nodes that cannot be part of the same information set because they involve different previous moves, making it impossible for the player to be unsure about which node they are at based on the game's history.

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}.

Accepted Answer

The Nash equilibrium strategy profile is {Up, Up} because neither player can improve their payoff by unilaterally changing their strategy.

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.

Accepted Answer

The answer of An improper subgame:
A) Occurs when a subroot...

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.

Accepted Answer

Total recall is characteristic of valid information sets and is also a feature of dynamic games with complete information. This means players remember all previous moves and have complete information about the game structure and payoffs.

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.

Accepted Answer

In repeated, static games with complete information, players remember all past actions and outcomes, which is what perfect recall entails.

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.

Accepted Answer

A valid information set in game theory represents a situation where a player has to make a decision without knowing the actions that have previously taken place. In the context of the static oil-drilling game, if the decision nodes D₂ and D₃ are collectively referred to, it implies that the player at that point does not know which path the game has taken to reach that node. This is a characteristic of a valid information set, where all the nodes within the set are indistinguishable to the player making the decision.

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.

Accepted Answer

The static oil-drilling game is an example of a Prisoner's dilemma, where two players face a situation where individual rationality leads to a worse outcome than mutual cooperation.

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.

Accepted Answer

In a static oil-drilling game, the Nash equilibrium occurs when both players choose strategies that are best responses to each other. If both players choose "Wide," neither can benefit by unilaterally changing their strategy, making {Wide, Wide} the Nash equilibrium.

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.

Accepted Answer

In a static game, players choose strategies simultaneously. The Nash equilibrium is where neither player can benefit by unilaterally changing their strategy. The payoff (24, 24) suggests mutual best responses.

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.

Accepted Answer

The probability of hiring a high-productivity worker who is a high school graduate is calculated by multiplying the overall probability of a worker being high-productivity (30%) by the probability that a high school graduate is high-productivity (60%). This gives 0.3 * 0.6 = 0.18 or 18%, which is not listed among the options provided. However, the question seems to be misinterpreted or the options may not accurately reflect the correct calculation based on the given information. The correct approach involves using the given probabilities directly related to the conditions specified, but the provided options and the calculation do not align with a standard interpretation of the question as it stands.

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.

Accepted Answer

The answer of 
-Consider the Spence Education Game depicted in...

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.

Accepted Answer

The answer of 
-Consider the Spence Education Game depicted in...

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.

Accepted Answer

The probability of hiring a low-productivity worker who is a college graduate is calculated as follows: Since 30% are high-productivity workers, 70% are low-productivity. Given a 75% probability of a college graduate being high-productivity, the probability of a college graduate being low-productivity is 1 - 0.75 = 0.25. Therefore, the probability is 0.25 * 70% = 17.5%. However, since the question asks for the probability of hiring a low-productivity worker who is a college graduate, we need to consider the total probability of hiring a college graduate, which is 0.3 (HP) * 0.75 + 0.7 (LP) * 0.25 = 0.225 + 0.175 = 0.4. Thus, the probability is 0.175 / 0.4 = 0.4375 or 44%.

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.

Accepted Answer

The answer of 
-Consider the Spence Education Game depicted in...

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.

Accepted Answer

The conditional expected payoff from hiring a college graduate is:(0.75 * 3,100) + (0.25 * 1,560) = 2,810

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.

Accepted Answer

The optimal hiring strategy for a risk-neutral firm would be to hire only college graduates, given the higher probability (75%) of hiring a high-productivity worker compared to hiring high-school graduates (60%). This strategy maximizes the expected productivity and, consequently, the expected payoff for the firm.

Quiz 16: Dynamic Games With Incomplete Information

In dynamic games with imperfect information:

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

An invalid information set:

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

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

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

An improper subgame:

Total recall:

Perfect recall:

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

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

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

-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:

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