Exam 16: Auctions-Part A

Herb's Auction House in Purloined Hubcap, Oregon, holds sealed-bid used-car auctions every Wednesday.Each car is sold to the highest bidder at the second-highest bidder's bid.On average, two-thirds of the cars that are auctioned are lemons and one-third are good used cars.A good car is worth $1,500 to any buyer.A lemon is worth only $150 to a buyer.Most buyers can do no better than random at picking good cars from the lot.There is only one exception, Al Crankcase.Al can sometimes but not always detect lemons by means of a subtle test.A good car will never fail Al's test, but approximately half of the lemons fail his test.Al attends every auction, tests every car, and always bids his expected value.Normal bidders bid less than the expected value for a randomly selected car but more than the value of a lemon.

A first edition of Adam Smith's Wealth of Nations (published in 1776)is being auctioned via the Internet.The current owner starts by posting his own "bid" for it.Bidders are allowed to submit bids at any time during a one-week interval.For the following week, bids will be accepted only if they exceed the currently posted high bid.Throughout the week, the highest bid that anyone has made so far will be posted.At the end of the week, the book will be sold to the highest bidder at the price that he or she bid for it.Assuming that bidders understand the rules of the auction, the outcome of this auction will be similar to that for

In a Dutch auction with rational bidders, it sometimes happens that the object being sold goes to someone whose value for the object is not as high as that of some other bidder(s).

The profit-maximizing strategy for a bidder in a Vickrey auction where there are common values for the object being sold is to bid less than her estimated value for the object, and the more bidders there are, the more the profit-maximizing bidder should shade her bid below her estimated value.

First Fiddler's Bank has foreclosed on a home mortgage and is selling the house at auction.There are three bidders for the house, Ernie, Minnie, and Betsy.First Fiddler's does not know the willingness to pay of these three bidders for the house, but on the basis of its previous experience, the bank believes that each of these bidders has a probability of 1/3 of valuing it at $700,000, a probability of 1/3 of valuing at $400,000, and a probability of 1/3 of valuing it at $300,000.First Fiddler's believes that these probabilities are independent among buyers.If First Fiddler's sells the house by means of a second-bidder, sealed-bid auction (Vickrey auction), what will be the bank's expected revenue from the sale? (Choose the closest option.)

If a good is sold in a Dutch auction and the bidders bid rationally, the price paid for the good will always be equal to the second-highest willingness to pay of auction participants.

A dealer decides to sell an oil painting by means of an English auction with a reservation price just slightly below $45,000.If he fails to get his reservation price for the painting, he will burn it.There are two bidders.The dealer believes that there are only three possible values, $90,000, $45,000, and $18,000, that each bidder's willingness to pay might take.Each bidder has a probability of 1/3 of having each of these willingnesses to pay, and the probabilities for each of the two bidders are independent of the other's valuation.Assuming that the two bidders bid rationally and do not collude, the dealer's expected revenue from selling the painting is slightly less than

An antique cabinet is being sold by means of an English auction.There are four bidders, Zelda, Clara, Anneli, and Diana.These bidders are unacquainted with each other and do not collude.Zelda values the cabinet at $800, Clara values it at $550, Anneli values it at $1,300, and Diana values it at $300.If the bidders bid in their rational self-interest, the cabinet will be sold to

An auction in which some bidders have different information about the value of an object than others is said to be an auction with private values.

First Fiddler's Bank has foreclosed on a home mortgage and is selling the house at auction.There are three bidders for the house, Ernie, Teresa, and Marilyn.First Fiddler's does not know the willingness to pay of these three bidders for the house, but on the basis of its previous experience, the bank believes that each of these bidders has a probability of 1/3 of valuing it at $600,000, a probability of 1/3 of valuing at $500,000, and a probability of 1/3 of valuing it at $200,000.First Fiddler's believes that these probabilities are independent among buyers.If First Fiddler's sells the house by means of a second-bidder, sealed-bid auction (Vickrey auction), what will be the bank's expected revenue from the sale? (Choose the closest option.)

A seller decides to sell an object by means of an English auction without a reservation price.There are two bidders.The seller believes that for each of the two bidders there is a probability of 1/2 that the bidder's value for the object is $400 and a probability of 1/2 that the bidder's value is $100.The seller believes that these probabilities are independent between bidders.If the bidders bid rationally, what is the seller's expected revenue from the auction?

The "winner's curse" refers to the fact that in a sealed-bid auction with private values, the winning bidder often pays more than he would have to in order to win the object auctioned.

A dealer decides to sell an antique automobile by means of an English auction with a reservation price of $2,700.There are two bidders.The dealer believes that there are only three possible values, $5,400, $3,600, and $2,700, that each bidder's willingness to pay might take.Each bidder has a probability of 1/3 of having each of these willingness to pay, and the probabilities for each of the two bidders are independent of the other's valuation.Assuming that the two bidders bid rationally and do not collude, the dealer's expected revenue from selling the car is approximately

The optimal strategy for a bidder in a private-values Vickrey auction is to bid his true valuation.

A seller decides to sell an object by means of an English auction without a reservation price.There are two bidders.The seller believes that for each of the two bidders there is a probability of 1/2 that the bidder's value for the object is $600 and a probability of 1/2 that the bidder's value is $200.The seller believes that these probabilities are independent between bidders.If the bidders bid rationally, what is the seller's expected revenue from the auction?

A seller knows that there are two bidders for the object he is selling.He believes that with probability 1/2, one has a buyer value of $5 and the other has a buyer value of $12 and, with probability 1/2, one has a buyer value of $10 and the other has a buyer value of $30.He knows that bidders will want to buy the object so long as they can get it for their buyer value or less.He sells it in an English auction with a reserve price which he must set before the auction starts.To maximize his expected profits, he should set the reserve price at