Question 1

An economics professor has devised an interesting game to test the understanding of his students. He randomly selects two students from his class and gives one of them a $50 bill. He then asks the student what percentage of the $50 she would give to her classmate. The first student can choose any percentage she wishes, while the second student can choose whether or not to accept the offer. If the second student does not accept the offer, the professor will take the bill back, but if he accepts the offer, the money will be divided in the ratio decided by the first student.
a) What is the likely outcome of this game if both students value more money to less?
b) What is the likely outcome of this game if the second student values fairness?

Accepted Answer

a) The first student is likely to offer the lowest possible amount to the second student. This is because the second student will always accept any offer made by the first student if he prefers more money to less. Given that her classmate will always accept her offer, the first student is better off by offering the lowest possible amount.
b) If the second student values fairness, he will not accept an unfair allotment of the money. If an unfair allotment is offered, neither of them will get any money. If the first student knows that the second student prefers fairness, then the first student has an incentive to offer a more equal allotment. If the first student offers to share the $50 bill in the ratio 1:1, the second student will consider it fair and accept the offer. Thus, the two students will receive $25 each in equilibrium.

Question 2

Two individuals are playing a trust game that has three rounds. In the first two rounds of the game, they have accumulated $1,000 as a team. In the third round, Player 1 is blindfolded and asked to decide whether he would let Player 2 guide him to a particular destination or opt out of the game. If he lets Player 2 guide him, Player 2 can either guide him to the correct destination or take him elsewhere. If she leads him to the correct destination, each of them will get half of the accumulated money. However, if Player 2 leads him astray, Player 2 will get 75 percent of the accumulated money and Player 1 will get 25 percent. If Player 1 opts out of the game, he will get 30 percent of the accumulated money and Player 2 will get 20 percent.
a) What is the equilibrium outcome in this case?
b) How will the equilibrium change if the players can impose a guilt penalty of 60 percent of the accumulated money on the defecting player?

Accepted Answer

a) In equilibrium, Player 1 will choose to opt out of the game. He will make this decision using backward induction. If he lets Player 2 guide him to the destination, Player 2 is likely to lead him astray, because Player 2 would earn 75 percent of the accumulated money by doing so, instead of the 50 percent she would earn by leading Player 1 to the correct destination. Given this information, Player 1 will choose to opt out of the game, as he will earn 30 percent of the accumulated money by doing so, instead of the 25 percent he would earn if Player 2 led him astray.
b) If the players can choose to impose a guilt penalty of 60 percent of the accumulated money, Player 1 will let Player 2 guide him, and Player 2 will guide him to the correct destination. In this case, Player 2 will get only 75 percent − 60 percent = 15 percent of the accumulated money if she leads Player 1 astray, while she will get 50 percent by guiding him to the correct destination. Therefore, she will always choose to guide him to the correct destination. Given this information, Player 1 will choose to be guided by Player 2, as he will get 50 percent of the accumulated money by doing so, instead of 30 percent if he opted out of the game.

Question 3

There are two players in a game. In each round of the game, one player has to trust the other for a particular task. In the first round, Player 1 has to decide whether she will trust Player 2. If she does not trust Player 2, she will get one-third of the prize money, while Player 2 will get the rest of the prize money. If she trusts Player 2, Player 2 can either cooperate with her or defect. If Player 2 defects, Player 1 will earn $0, while Player 2 will get the entire prize money. If Player 2 cooperates, each of them will get half the prize money. What will the equilibrium outcome of this game be if Player 1 can impose a guilt penalty of two-thirds of the prize money and is known to be a vengeful player?

Accepted Answer

If there is no guilt penalty, in equilibrium, Player 1 will not trust Player 2. She will make this decision using backward induction. If she trusts Player 2, Player 2 is likely to defect, because he will earn the entire prize money in that case, while he will earn only half of the money by cooperating. Given this information, Player 1 will not trust him, as she will not earn any money if she trusts him, while she will earn one-third of the money if she does not trust him. However, if there is a guilt penalty of two-thirds of the prize money, Player 2 will choose to cooperate, because he will earn a lower payoff by defecting. Given this information, Player 1 will trust him, and each of them will get half of the money.

Question 4

Four friends-Tom, Bill, Jeff, and Roger-are participating in an English auction. Tom values the good being auctioned at $500, Bill values it at $210, Jeff values it at $350, and Roger values it at $625.
-Refer to the scenario above. If they are the only bidders in the auction, Jeff will win the auction if ________.

Accepted Answer

In an English auction, the highest bidder wins. If Tom and Roger stop bidding at $100 and $200, respectively, and Bill bids up to his value ($210), Jeff, who values the good at $350, can win by bidding just above $210, since no one else is willing to bid higher.

Question 5

Alice is participating in a Dutch auction for a painting. There are five other bidders, and Alice values the painting at $30,000.
-Refer to the scenario above. What is Alice's optimal bidding price?

Accepted Answer

Alice should bid the highest price she is willing to pay, which is $30,000, but in a Dutch auction, she should aim to bid slightly below her valuation to maximize her surplus, so $25,000 is optimal if she believes it will still win the auction.

Question 6

Alice is participating in a Dutch auction for a painting. There are five other bidders, and Alice values the painting at $30,000.
-Refer to the scenario above. If Alice wins the auction, the seller earns an average revenue of ________.

Accepted Answer

The answer of Alice is participating in a Dutch auction...

Question 7

Rebecca is participating in a Dutch auction for an antique necklace. The total number of bidders in this auction is ten. Rebecca values the necklace at $45,000, while all the other bidders value it below $45,000.
-Refer to the scenario above. If the best response of one bidder is to place a bid of $9,000, what is her maximum willingness to pay for the necklace?

Accepted Answer

In a Dutch auction, the auctioneer starts with a high asking price which is gradually lowered until some participant is willing to accept the auctioneer's price, or a predetermined minimum price is reached. If a bidder's best response is to place a bid of $9,000, it means this is the highest price at which they are willing to buy the necklace before someone else does, indicating their maximum willingness to pay is slightly above $9,000, hence $10,000.

Question 8

Rebecca is participating in a Dutch auction for an antique necklace. The total number of bidders in this auction is ten. Rebecca values the necklace at $45,000, while all the other bidders value it below $45,000.
-Refer to the scenario above. Rebecca should place a bid of ________.

Accepted Answer

In a Dutch auction, the price starts high and decreases until a bidder accepts the current price. Since Rebecca values the necklace at $45,000 and all other bidders value it less, she should bid just above the highest valuation of the other bidders, which is below $45,000. Therefore, $40,500 is a strategic bid.

Question 9

Rebecca is participating in a Dutch auction for an antique necklace. The total number of bidders in this auction is ten. Rebecca values the necklace at $45,000, while all the other bidders value it below $45,000.
-Refer to the scenario above. The seller will earn a revenue of ________.

Accepted Answer

In a Dutch auction, the price starts high and decreases until a bidder accepts the current price. Since Rebecca values the necklace at $45,000 and all other bidders value it less, she will win the auction at the highest price below $45,000 that she is willing to pay, which is typically just above the second-highest valuation. However, since no other bidder values it above $40,500, she will likely pay $40,500.

Question 10

Rebecca is participating in a Dutch auction for an antique necklace. The total number of bidders in this auction is ten. Rebecca values the necklace at $45,000, while all the other bidders value it below $45,000.
-Refer to the scenario above. If the number of participants in the auction increases to twenty, Rebecca should place a bid of ________.

Accepted Answer

The answer of Rebecca is participating in a Dutch auction...

Question 11

Rebecca is participating in a Dutch auction for an antique necklace. The total number of bidders in this auction is ten. Rebecca values the necklace at $45,000, while all the other bidders value it below $45,000.
-Refer to the scenario above. If Rebecca wins the auction, she will earn a surplus of ________.

Accepted Answer

The answer of Rebecca is participating in a Dutch auction...

Question 12

Which of the following is a difference between an English auction and a Dutch auction?

Accepted Answer

An English auction is characterized by ascending bids where the price is increased until only one bidder remains, while a Dutch auction features a descending price where the auction starts at a high price and decreases until a bidder accepts the price.

Question 13

Consider the following situation. Molly is one among the sixty‐one bidders who take part in a first‐price auction for vintage furniture. Molly places a value of $850, the highest value, for a vintage dressing table that comes up for auction. Joseph has the second‐highest willingness to pay of $750
-Refer to the scenario above. If the number of bidders goes up to 65, Molly's optimal bid for the product would be ________, and her consumer surplus would be ________.

Accepted Answer

Molly's optimal bid is the second highest value, which is $750. Her consumer surplus is the difference between her value and her bid, which is $850 - $750 = $100.

Quiz 14: Social Economics and Auctions and Bargaining

Alice is participating in a Dutch auction for a painting. There are five other bidders, and Alice values the painting at $30,000. -Refer to the scenario above. What is Alice's optimal bidding price?

Alice is participating in a Dutch auction for a painting. There are five other bidders, and Alice values the painting at $30,000. -Refer to the scenario above. If Alice wins the auction, the seller earns an average revenue of ________.

Rebecca is participating in a Dutch auction for an antique necklace. The total number of bidders in this auction is ten. Rebecca values the necklace at $45,000, while all the other bidders value it below $45,000. -Refer to the scenario above. Rebecca should place a bid of ________.

Rebecca is participating in a Dutch auction for an antique necklace. The total number of bidders in this auction is ten. Rebecca values the necklace at $45,000, while all the other bidders value it below $45,000. -Refer to the scenario above. The seller will earn a revenue of ________.

Which of the following is a difference between an English auction and a Dutch auction?