Exam 16: Auctions

A dealer decides to sell an antique automobile by means of an English auction with a reservation price of $1,800. There are two bidders. The dealer believes that there are only three possible values, $6,300, $3,600, and $1,800, that each bidder's willingness to pay might take. Each bidder has a probability of 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 car is approximately

In a private-values auction with rational bidders, we can expect the same outcome from an English auction as from a Vickrey auction.

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 $54,000. 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, $54,000, and $45,000, that each bidder's willingness to pay might take. Each bidder has a probability of 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

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 of valuing it at $600,000, a probability of of valuing at $500,000, and a probability of 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 that the bidder's value for the object is $600 and a probability of 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 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 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

In an English auction, with rational bidders, the object being sold always goes to the bidder who values it most highly.

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

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.

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.

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 that the bidder's value for the object is $400 and a probability of 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?

A dealer decides to sell an antique automobile by means of an English auction with a reservation price of $900. There are two bidders. The dealer believes that there are only three possible values, $7,200, $3,600, and $900, that each bidder's willingness to pay might take. Each bidder has a probability of 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 car is approximately

It is never a profit-maximizing strategy for a seller in an English auction to set a reserve price for the good he is selling so high that he might not be able to sell it at all.

It is often the case that a seller can increase his profit from an auction by setting a reserve price even if he has to destroy the object being auctioned if nobody bids as high as the reserve price.