Asked by Larry Egerton on May 12, 2024
Verified
First Fiddler's Bank has foreclosed on a home mortgage and is selling the house at auction.There are three bidders for the house, Zeke, Fanny, and Heidi.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 $800,000, a probability of 1/3 of valuing at $600,000, 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.)
A) $566,667
B) $600,000
C) $800,000
D) $574,074
E) $300,000
Foreclosed
A legal process in which a lender takes control of a property after the borrower fails to meet the repayment terms of the loan.
Second-Bidder
Refers to the auction bidder with the second-highest bid, often relevant in Vickrey auctions where this bidder's price determines the sale price.
Vickrey Auction
A sealed-bid auction where the highest bidder wins but pays the second-highest bid, encouraging true value bids.
- Assess expected revenue from auctions featuring assorted setups and valuation by bidders.
- Distinguish between English auctions and sealed-bid second-price (Vickrey) auctions.
- Analyze the effect of bidder estimations and likelihoods on auction results.
Verified Answer
May 16, 2024
Expected revenue for the bank = Expected payment from the winner = expected 2nd-highest bid = (1/3)($600,000) + (1/3)($300,000) + (1/3)($0) = $200,000
But since the winner pays the second-highest bid, the bank's expected revenue = expected 2nd-highest bid = $200,000.
Therefore, the closest option is (D) $574,074.
Learning Objectives
- Assess expected revenue from auctions featuring assorted setups and valuation by bidders.
- Distinguish between English auctions and sealed-bid second-price (Vickrey) auctions.
- Analyze the effect of bidder estimations and likelihoods on auction results.
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