Deck 13: Pure Strategies With Uncertain Payoffs

Question 1

Uncertainty refers to:

A) An unknown outcome involving risky choices.
B) Multiple outcomes with unknown or meaningless probabilities.
C) Multiple outcomes with known and meaningful probabilities.
D) Random and risky states of nature.
E) All of the above.

Answer 1

Multiple outcomes with unknown or meaningless probabilities.

Question 2

Risk refers to:

A) An unknown outcome involving risky choices.
B) Multiple outcomes with unknown or meaningless probabilities.
C) Multiple outcomes with known and meaningful probabilities.
D) Random and risky states of nature.
E) None of the above.

Answer 2

Multiple outcomes with known and meaningful probabilities.

Question 3

A risk averse individual tends to exhibit _____ marginal utility of money.

A) diminishing
B) constant
C) increasing
D) indifferent
E) inverted

Answer 3

diminishing

Question 4

A risk loving individual tends to exhibit _____ marginal utility of money.

A) diminishing
B) constant
C) increasing
D) indifferent
E) inverted

Question 5

A risk neutral individual tends to exhibit _____ marginal utility of money.

A) diminishing
B) constant
C) increasing
D) indifferent
E) inverted

Question 6

Risk aversion can best be explained by:

A) A person's level of income.
B) Increasing marginal utility of money.
C) The size of the bet.
D) Diminishing marginal utility of money.
E) Constant marginal utility of money.

Question 7

A fair gamble is one in which:

A) The expected payoff of a bet is zero.
B) There is an equal probability of winning or losing a bet.
C) The expected payoff from a bet is equal to the bet itself.
D) The expected payoff from a bet is greater than zero.
E) Answers a and c are correct.

Question 8

A risk averse individual:

A) Will always accept a fair gamble.
B) Will not accept a fair gamble for large bets.
C) Will sometimes accept a fair gamble for very small bets.
D) Answers b and c are correct.
E) All of the above are correct.

Question 9

The standard statistical measure of risk is:

A) Expected value (mean).
B) Coefficient of variation.
C) Coefficient of determination.
D) Standard deviation.
E) Variance.

Question 10

Suppose that an individual's utility of money function is U = 5M ². This individual can best be described as risk:

A) Indifferent.
B) Averse.
C) Neutral.
D) Loving.
E) None of the above.

Question 11

Suppose that an individual's utility of money function is U = 10M ^0.5. This individual can best be described as risk:

A) Indifferent.
B) Averse.
C) Neutral.
D) Loving.
E) None of the above.

Question 12

Suppose that an individual's utility of money function is U = 0.5M. This individual can best be described as risk:

A) Indifferent.
B) Averse.
C) Neutral.
D) Loving.
E) None of the above.

Question 13

Suppose that an individual's utility of money function is U = 25M. This individual can best be described as risk:

A) Indifferent.
B) Averse.
C) Neutral.
D) Loving.
E) None of the above.

Question 14

Suppose that an individual's utility of money function is U = M ^2/5. This individual can best be described as risk:

A) Indifferent.
B) Averse.
C) Neutral.
D) Loving.
E) None of the above.

Question 15

Suppose that an individual's utility of money function is U = 5M ⁵. This individual can best be described as risk:

A) Indifferent.
B) Averse.
C) Neutral.
D) Loving.
E) None of the above.

Question 16

Suppose that an individual's utility of money function is U = 0.65M ^0.75. This individual can best be described as risk:

A) Indifferent.
B) Averse.
C) Neutral.
D) Loving.
E) None of the above.

Question 17

Suppose that Professor Nash is planning to attend a 10 day academic conference. His utility function for the trip is U = T ², where T is the length of the conference in days. Professor Nash is concerned that he will be forced to leave the conference early due to an illness in his family. The probability that Professor Nash will have go home is 40 percent. The expected utility of this trip is:

A) 4.
B) 8.
C) 10.
D) 40.
E) 100.

Question 18

Suppose that Professor Nash is planning to attend a 10 day academic conference. His utility function for the trip is U = T ², where T is the length of the conference in days. Professor Nash is concerned that he will be forced to leave the conference early due to an illness in his family. The probability that Professor Nash will have go home is 40 percent. Professor Nash can best be described as:

A) A risk lover.
B) A risk hater.
C) Being indifferent to risk.
D) A person who would not accept a fair gamble.
E) As someone who hates to travel.

Question 19

Suppose that Mr. Kent is planning to fly to Kansas to visit his silver-haired mother for 16days. Mr. Kent lives in New York City and will depart from LaGuardia airport. Mr.Kent's utility function for the trip is U = 2T ^1/2, where T is the length of the visit in days. Due to chronic congestion and weather delays there is a 10 percent probability that the flight will be cancelled and Mr. Kent is forced to cancel his trip. Mr. Kent can best be describes as:

A) A risk hater.
B) A risk taker.
C) A person who will accept a fair gamble.
D) A risk averse individual.
E) As someone who does not like traveling to Kansas.

Question 20

Suppose that Mr. Kent is planning to fly to Kansas to visit his silver-haired mother for 16days. Mr. Kent lives in New York City and will depart from LaGuardia airport. Mr.Kent's utility function for the trip is U = 2T ^1/2, where T is the length of the visit in days. Due to chronic congestion and weather delays there is a 10 percent probability that the flight will be cancelled and Mr. Kent is forced to cancel his trip. The expected utility of this trip is:

A) 0.8.
B) 1.6.
C) 3.2.
D) 6.4.
E) None of the above.

Question 21

Suppose that a raffle ticket costs $5 and there is a 99 percent chance of not winning. For this raffle to be considered a fair gamble, the winning prize must be worth:

A) $50.
B) $100.
C) $500.
D) $1,000.
E) $5,000.

Question 22

Suppose that a raffle ticket costs $5 and has a jackpot of $1 million. For this raffle to be considered a fair gamble, the probability of not winning must be:

A) 99.95 percent.
B) 99.995 percent.
C) 99.9995 percent.
D) 99.99995 percent.
E) None of the above.

Question 23

Suppose that a raffle ticket costs $10 and there is an 80 percent chance of not winning. For this raffle to be considered a fair gamble, the winning prize must be worth:

A) $50.
B) $100.
C) $150.
D) $200.
E) $250.

Question 24

Suppose that a raffle ticket costs $10 and has a jackpot of $2,500. For this raffle to be considered a fair gamble, the probability of not winning must be:

A) 40 percent.
B) 60 percent.
C) 96 percent.
D) 99.6 percent.
E) 99.96 percent.

Question 25

Gog is offered the following wager by Magog. For a payment of $10, Gog can blindfolded draw a single marble from an urn containing ten marbles. Eight marbles are green and two are red. If Gog selects the green marble, he wins $500. If he draws a red marble, he loses $125. The expected value of this gamble is:

A) !$10.
B) $0.
C) $10.
D) $90.
E) $100.

Question 26

Gog is offered the following wager by Magog. For a payment of $10, Gog can blindfolded draw a single marble from an urn containing ten marbles. Eight marbles are green and two are red. If Gog selects the green marble, he wins $500. If he draws a red marble, he loses $125. Which of the following statements is correct?

A) If Gog is risk averse, he will accept this fair gamble.
B) If Gog is risk averse, he will not accept this fair gamble.
C) If Gog is risk neutral, he will accept this unfair gamble.
D) If Gog is risk loving, he may or may not accept this fair gamble.
E) If Gog is risk loving, he may or may not accept this unfair gamble.

Question 27

Bob is offered the following wager by Nabob. For a payment of $20, Bob can flip five fair coins. If Bob flips three or more heads he wins $100, otherwise he loses $100. The expected value of this wager is:

A) $0.
B) $40.
C) $60.
D) $80.
E) $100.

Question 28

Bob is offered the following wager by Nabob. For a payment of $20, Bob can flip five fair coins. If Bob flips three or more heads he wins $100, otherwise he loses $100. Which of the following statements is correct?

A) If Bob is risk averse, he will accept this fair gamble.
B) If Bob is risk averse, he will not accept this fair gamble.
C) If Bob is risk averse, he will not accept this unfair gamble.
D) If Bob is risk neutral, he will not accept this fair gamble.
E) Answers b and d are correct.

Question 29

Uncertainty can be introduced into games by:

A) Reducing risk.
B) Forcing one of the players to adopt a strictly dominated strategy.
C) Utilizing empty threats.
D) Assigning probabilities to the payoffs from alternative strategy profiles.
E) Randomly choosing a strategy, such as by rolling a pair of fair dice.

Question 30

s

-Consider the game depicted in Figure 13.1, which summarizes the payoffs from alternative strategy profiles from an optimistic state of nature. The Nash equilibrium strategy profile is:

A) {A1, B1}.
B) {A2, B2}.
C) {A3, B3}.
D) This game does not have a Nash equilibrium.
E) This game has multiple Nash equilibria.

Question 31

-Consider the game depicted in Figure 13.2 in which, which summarizes the payoffs from alternative strategy profiles from a pessimistic state of nature. The Nash equilibrium strategy profile is:

A) {A1, B1}.
B) {A2, B2}.
C) {A3, B3}.
D) This game does not have a Nash equilibrium.
E) This game has multiple Nash equilibria.

Question 32

s

-Consider Figure 13.1, which represents an optimistic state of nature and Figure 13.2, which represents a pessimistic state of nature. Suppose that there is a 10 percent probability of an optimistic state of nature and a 90 percent probability of a pessimistic state of nature. The Nash equilibrium strategy profile for this game is:

A) {A1, B1}.
B) {A2, B2}.
C) {A3, B3}.
D) This game does not have a Nash equilibrium.
E) This game has multiple Nash equilibria.

Question 33

s

-Consider Figure 13.1, which represents an optimistic state of nature and Figure 13.2, which represents a pessimistic state of nature. Suppose that there is a 10 percentprobability of an optimistic state of nature and a 90 percent probability of a pessimistic state of nature will prevail. The expected payoffs to both players in this game are:

A) (71, 71).
B) (81, 81).
C) (91, 91).
D) (101, 101).
E) None of the above.

Question 34

s

-Consider Figure 13.1, which represents an optimistic state of nature and Figure 13.2, which represents a pessimistic state of nature. Suppose that there is a 10 percent probability of an optimistic state of nature and a 90 percent probability of a pessimistic state of nature will prevail. The actual payoffs to both players in this game are:
I. (70, 70).
II. (80, 80).
III. (90, 90).
IV. (100, 100).
Which of the following is the correct answer?

A) I or II.
B) II or III.
C) III or IV.
D) I or III.
E) I or IV.

Question 35

-Consider the game depicted in Figure 13.3, which summarizes the payoffs fromalternative strategy profiles from state of nature X. The Nash equilibrium strategy profile is:

A) {A1, B2}.
B) {A2, B3}.
C) {A3, B3}.
D) {A3, B1}.
E) {A2, B1}.

Question 36

-Consider the game depicted in Figure 13.4, which summarizes the payoffs from alternative strategy profiles from state of nature Y. The Nash equilibrium strategy profile is:

A) {A1, B1}.
B) {A2, B2}.
C) {A3, B3}.
D) {A3, B2}.
E) {A2, B1}.

Question 37

-Consider the games depicted in Figures 13.3 and 13.4. Suppose that there is a 60 percent probability that state of nature X will prevail and a 40 percent probability that state of nature Y will prevail. The expected payoffs to both players in this game are:

A) (16, 12.8).
B) (13.6, 15.4).
C) (20, 14).
D) (5, 16.8).
E) (14.4, 14).

Question 38

-Consider the games depicted in Figures 13.3 and 13.4. Suppose that there is a 60 percent probability that state of nature X will prevail and a 40 percent probability that state of nature Y will prevail. The actual payoffs to both players in this game are:
I. (12, 15).
II. (16, 16).
III. (40, 12).
IV. (12, 20).
Which of the following is correct?

A) I or II.
B) II or III.
C) II or IV.
D) I or III.
E) I or IV.

Question 39

-Consider Figure 13.5, which depicts the risk-return indifference curves for three investors. If the projects are mutually exclusive, which project has the highest expected rate of return for investor 3?

A) A
B) B
C) C
D) D
E) E

Question 40

-Consider Figure 13.5, which depicts the risk-return indifference curves for three investors. If the projects are mutually exclusive, which project has the highest expected rate of return for investor 1?

A) A
B) B
C) C
D) D
E) E

Question 41

-Consider Figure 13.5, which depicts the risk-return indifference curves for three investors. If the projects are mutually exclusive, which is the most preferred for investor 2?

A) A
B) B
C) C
D) D
E) E

Question 42

-Consider Figure 13.5, which depicts the risk-return indifference curves for threeinvestors. If the projects are mutually exclusive, which is the most preferred for investor 3?

A) A
B) B
C) C
D) D
E) E

Question 43

-Consider Figure 13.5, which depicts the risk-return indifference curves for threeinvestors. If the projects are mutually exclusive, which is the most preferred for investor 1?

A) A
B) B
C) C
D) D
E) E

Question 44

-Consider Figure 13.5, which depicts the risk-return indifference curves for three investors. If the projects are mutually exclusive, which is the least risky for investor 1?

A) A
B) B
C) C
D) D
E) E

Question 45

-Consider Figure 13.5, which depicts the risk-return indifference curves for three investors. If the projects are mutually exclusive, for which project is investor 1 indifferent between accepting and rejecting?

A) A
B) B
C) C
D) D
E) E

Question 46

-Consider Figure 13.5, which depicts the risk-return indifference curves for three investors. If the projects are mutually exclusive, for which project is investor 2 indifferent between accepting and rejecting?

A) A
B) B
C) C
D) D
E) E

Question 47

-Consider Figure 13.5, which depicts the risk-return indifference curves for three investors. If the projects are mutually exclusive, for which project is investor 3 indifferent between accepting and rejecting?

A) A
B) B
C) C
D) D
E) E

Question 48

-Consider Figure 13.5, which depicts the risk-return indifference curves for three investors. If the projects are mutually exclusive, which investor is the most risk averse?
I. 1
II. 2
III. 3
Which of the following is correct?

A) I only
B) II only
C) III only
D) I or II.
E) I, II, and III.

Question 49

-Consider Figure 13.5, which depicts the risk-return indifference curves for three investors. If the projects are mutually exclusive, which investor is the least risk averse?
I. 1
II. 2
III. 3
Which of the following is correct?

A) I only
B) II only
C) III only
D) I or II.
E) I, II, and III.

Question 50

188

-Consider the pricing game depicted in Figure 13.6. Payoffs are in millions of dollars. Suppose that firm A believes that regardless of its strategy, there is a 15 percent chance that firm B will charge a high price and an 85 percent chance that firm B will charge a low price. If firm A is risk neutral, what is the subgame perfect equilibrium for this game?

A) {High price 6 High price}
B) {High price 6 Low price}
C) {Low price 6 High price}
D) {Low price 6 Low price}

Question 51

188

-Consider the pricing game depicted in Figure 13.6. Payoffs are in millions of dollars. Suppose that firm A believes that regardless of its strategy, there is a 15 percent chance that firm B will charge a high price and an 85 percent chance that firm B will charge a low price. What is the riskier strategy profile for firm A?

A) {High price 6 High price}
B) {High price 6 Low price}
C) {Low price 6 High price}
D) {Low price 6 Low price}

Question 52

188

-Consider the pricing game depicted in Figure 13.6. Payoffs are in millions of dollars. Suppose that firm A believes that regardless of its strategy, there is a 85 percent chance that firm B will charge a high price and an 15 percent chance that firm B will charge a low price. If firm A is risk neutral, what is the subgame perfect equilibrium for this game?

A) {High price 6 High price}
B) {High price 6 Low price}
C) {Low price 6 High price}
D) {Low price 6 Low price}

Question 53

188

-Consider the pricing game depicted in Figure 13.6. Payoffs are in millions of dollars. Suppose that firm A believes that regardless of its strategy, there is a 85 percent chance that firm B will charge a high price and an 15 percent chance that firm B will charge a low price. What is the riskier strategy profile for firm A?

A) {High price 6 High price}
B) {High price 6 Low price}
C) {Low price 6 High price}
D) {Low price 6 Low price}

Question 54

188

-Consider the pricing game depicted in Figure 13.6. Payoffs are in millions of dollars. Suppose that if firm A charges a high price there is a 15 percent chance that firm B will charge a high price and an 85 percent chance that firm B will charge a low price. Suppose that if firm A charges a low price there is an 85 percent chance that firm B will charge a high price and a 15 percent chance that firm B will charge a low price. If firm A is risk neutral, what is the subgame perfect equilibrium for this game?

A) {High price 6 High price}
B) {High price 6 Low price}
C) {Low price 6 High price}
D) {Low price 6 Low price}

Question 55

188

-Consider the pricing game depicted in Figure 13.6. Suppose that if firm A charges a high price there is a 15 percent chance that firm B will charge a high price and an 85 percent chance that firm B will charge a low price. If firm A charges a low price there is an 85 percent chance that firm B will charge a high price and a 15 percent chance that firm B will charge a low price. What is the riskier strategy profile for firm A?

A) {High price 6 High price}
B) {High price 6 Low price}
C) {Low price 6 High price}
D) {Low price 6 Low price}

Question 56

-Consider the pricing game depicted in Figure 13.7. Payoffs are in millions of dollars. Suppose that firm A believes that regardless of its strategy, there is a 25 percent chance that firm B will charge a high price and an 75 percent chance that firm B will charge a low price. If firm A is risk neutral, what is the subgame perfect equilibrium for this game?

A) {High price 6 High price}
B) {High price 6 Low price}
C) {Low price 6 High price}
D) {Low price 6 Low price}

Question 57

-Consider the pricing game depicted in Figure 13.7. Payoffs are in millions of dollars. Suppose that firm A believes that regardless of its strategy, there is a 25 percent chance that firm B will charge a high price and an 75 percent chance that firm B will charge a low price. What is the riskier strategy profile for firm A?

A) {High price 6 High price}
B) {High price 6 Low price}
C) {Low price 6 High price}
D) {Low price 6 Low price}

Question 58

-Consider the pricing game depicted in Figure 13.7. Payoffs are in millions of dollars. Suppose that firm A believes that regardless of its strategy, there is a 75 percent chance that firm B will charge a high price and an 25 percent chance that firm B will charge a low price. If firm A is risk neutral, what is the subgame perfect equilibrium for this game?

A) {High price 6 High price}
B) {High price 6 Low price}
C) {Low price 6 High price}
D) {Low price 6 Low price}

Question 59

-Consider the pricing game depicted in Figure 13.7. Payoffs are in millions of dollars. Suppose that firm A believes that regardless of its strategy, there is a 75 percent chance that firm B will charge a high price and an 25 percent chance that firm B will charge a low price. What is the riskier strategy profile for firm A?

A) {High price 6 High price}
B) {High price 6 Low price}
C) {Low price 6 High price}
D) {Low price 6 Low price}

Question 60

-Consider the game depicted in Figure 13.7 Payoffs are in millions of dollars. Suppose that if firm A charges a high price there is a 25 percent chance that firm B will charge a high price and an 75 percent chance that firm B will charge a low price. If firm A charges a low price there is an 75 percent change that firm B will charge a high price and a 25 percent chance that firm B will charge a low price. If firm A is risk neutral, what is the subgame perfect equilibrium for this game?

A) {High price 6 High price}
B) {High price 6 Low price}
C) {Low price 6 High price}
D) {Low price 6 Low price}

Question 61

-Consider the game depicted in Figure 13.7 Payoffs are in millions of dollars. Suppose that if firm A charges a high price there is a 25 percent chance that firm B will charge a high price and an 75 percent chance that firm B will charge a low price. If firm A charges a low price there is an 75 percent change that firm B will charge a high price and a 25 percent chance that firm B will charge a low price. What is the riskier strategy profile for firm A?

A) {High price 6 High price}
B) {High price 6 Low price}
C) {Low price 6 High price}
D) {Low price 6 Low price}

Question 62

-Consider the entry advertising game depicted in Figure 13.8. Payoffs are in thousands of dollars. Suppose that there is a 70 percent probability that Goliath will advertize on the radio and an 30 percent probability that Goliath will advertise in newspapers regardless of the advertizing strategy adopted by David. If David is risk neutral, what is the subgame perfect equilibrium for this game?

A) {TV 6 Radio}
B) {TV 6 Newspapers}
C) {Magazines 6 Radio}
D) {Magazin es 6 Newspapers}

Question 63

-Consider the entry advertising game depicted in Figure 13.8. Payoffs are in thousands of dollars. Suppose that there is a 70 percent probability that Goliath will advertize on the radio and an 30 percent probability that Goliath will advertize in newspapers regardless of the advertizing strategy adopted by David. What is the riskier strategy profile for David?

A) {TV 6 Radio}
B) {TV 6 Newspapers}
C) {Magazines 6 Radio}
D) {Magazines 6 Newspapers}

Question 64

-Consider the entry advertising game depicted in Figure 13.8. Payoffs are in thousands of dollars. If David advertizes on TV, there is a 70 percent probability that Goliath will advertize on the radio and an 30 percent probability that Goliath will advertize in newspapers. If David advertizes in magazines, there is a 50 percent probability that Goliath will advertize on the radio or in newspapers. If David is risk neutral, what is the subgame perfect equilibrium for this game?

A) {TV 6 Radio}
B) {TV 6 Newspapers}
C) {Magazines 6 Radio}
D) {Magazines 6 Newspapers}

Question 65

-Consider the entry advertising game depicted in Figure 13.8. Payoffs are in thousands of dollars. If David advertizes on TV, there is a 70 percent probability that Goliath will advertize on the radio and an 30 percent probability that Goliath will advertize in newspapers. If David advertizes in magazines, there is a 50 percent probability that Goliath will advertize on the radio or in newspapers. What is the riskier strategy profile for David?

A) {TV 6 Radio}
B) {TV 6 Newspapers}
C) {Magazines 6 Radio}
D) {Magazines 6 Newspapers}