Question 1

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:

Accepted Answer

For a gamble to be considered fair, the expected value of participating should be equal to the cost of participation. Here, with a 99% chance of losing ($5 loss) and a 1% chance of winning, the expected value (EV) can be calculated as: EV = (0.01 * Prize) - (0.99 * $5). Setting EV equal to the cost of the ticket ($5) and solving for the Prize gives: $5 = (0.01 * Prize) - $4.95, which simplifies to Prize = $500.

Question 2

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:

Accepted Answer

For a fair gamble, the expected value should equal the cost of the ticket. If the jackpot is $1 million and the ticket costs $5, the probability of winning should be 0.000005 (or 0.0005%) to make the expected value $5. Therefore, the probability of not winning is 1 - 0.000005 = 0.999995 or 99.9995%.

Question 3

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:

Accepted Answer

The expected value of the raffle ticket is 0.8 * (-$10) + 0.2 * $x = 0, where x is the winning prize. Solving for x, we get x = $50.

Question 4

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:

Accepted Answer

For a fair gamble, the expected value should be zero. If the ticket costs $10 and the jackpot is $2,500, the probability of winning should be 0.004 (1/250) to make the expected value zero. Therefore, the probability of not winning is 1 - 0.004 = 0.996 or 99.6 percent.

Question 5

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:

Accepted Answer

The answer of Gog is offered the following wager by...

Question 6

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?

Accepted Answer

The answer of Gog is offered the following wager by...

Question 7

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:

Accepted Answer

The expected value is calculated by considering the probabilities of winning and losing. The probability of getting 3 or more heads in 5 flips of a fair coin is 0.5. The expected value is (0.5 * $100) + (0.5 * -$100) = $0.

Question 8

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?

Accepted Answer

The answer of Bob is offered the following wager by...

Question 9

Uncertainty can be introduced into games by:

Accepted Answer

Assigning probabilities to the payoffs from alternative strategy profiles introduces uncertainty into games.

Question 10

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:

Accepted Answer

A Nash equilibrium occurs when each player's strategy is the best response to the other player's strategy. In the given game, {A2, B2} is the strategy profile where neither player can benefit by unilaterally changing their strategy, making it the Nash equilibrium.

Question 11

-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:

Accepted Answer

A Nash equilibrium occurs when each player's strategy is optimal given the other player's strategy. In the strategy profile {A2, B2}, neither player can benefit by unilaterally changing their strategy, making it a Nash equilibrium.

Question 12

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:

Accepted Answer

The answer of  s
-Consider Figure 13.1, which represents an...

Question 13

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:

Accepted Answer

The answer of  s
-Consider Figure 13.1, which represents an...

Question 14

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?

Accepted Answer

Given the probabilities, the expected payoff is calculated by weighing the optimistic and pessimistic outcomes. The optimistic state (higher payoffs) is less likely, so the higher payoffs (III or IV) are more probable in this context.

Question 15

-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:

Accepted Answer

In a Nash equilibrium, each player's strategy is the best response to the other player's strategy. For {A3, B3}, neither player can unilaterally change their strategy to get a better payoff, making it the Nash equilibrium.

Question 16

-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:

Accepted Answer

The answer of 
-Consider the game depicted in Figure 13.4,...

Question 17

-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:

Accepted Answer

The answer of 
-Consider the games depicted in Figures 13.3...

Question 18

-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?

Accepted Answer

The answer of 
-Consider the games depicted in Figures 13.3...

Question 19

-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?

Accepted Answer

Project A has the highest expected rate of return for investor 3 because it is the project that is located on the highest indifference curve for investor 3.

Question 20

-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?

Accepted Answer

Without seeing Figure 13.5, we can deduce that the correct answer is based on the specific preferences of investor 1 as indicated in the question. Since the question asks for the project with the highest expected rate of return for investor 1 and given that projects are mutually exclusive, we must assume that project A is positioned in such a way on the risk-return spectrum that it aligns with investor 1's highest level of return preference among the given options. This is a common type of question in finance where investors' risk-return indifference curves help determine their preferred investments.

Quiz 13: Pure Strategies With Uncertain Payoffs

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:

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:

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:

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:

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:

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?

Uncertainty can be introduced into games by:

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:

-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:

-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:

-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:

-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:

-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?

-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?