Exam 18:Auctions-Part B

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An antique cabinet is being sold by means of an English auction.There are four bidders,Arabella,Lana,Hester,and Betsy.These bidders are unacquainted with each other and do not collude.Arabella values the cabinet at $1,000,Lana values it at $500,Hester values it at $1,300,and Betsy values it at $800.If the bidders bid in their rational self-interest,the cabinet will be sold to

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A dealer decides to sell an oil painting by means of an English auction with a reservation price of slightly below $75,000.If she fails to get a bid as high as her reservation price,she will burn the painting.There are two bidders.The dealer believes that each bidder's willingness to pay will take one of the three following values: $90,000,$75,000,and $30,000.The dealer believes that each bidder has a probability of 1/3 of having each of these three values.The probability distribution of each buyer's value is independent of that of the other's.Assuming that the two bidders bid rationally and do not collude,the dealer's expected revenue from selling the painting is slightly less than

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Jerry'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,2/3 of the cars that are auctioned are lemons and 1/3 are good used cars.A good used car is worth $3,000 to any buyer.A lemon is worth $150 to any buyer.Most buyers can do no better than picking at random from among these used cars.The only exception is Al Crankcase.Recall that Al can sometimes detect lemons by tasting the oil on the car's dipstick.A good car never fails Al's test,but half of the lemons fail his test.Al attends every auction,licks every dipstick,and bids his expected value of every car given the results of his test.Al will bid

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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 that each bidder's willingness to pay might take,$6,700,$3,400,and $900.Each bidder has a probability of 1/3 of having each of these willingnesses to pay,and the probabilities 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 automobile is

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A dealer decides to sell an oil painting by means of an English auction with a reservation price of slightly below $70,000.If she fails to get a bid as high as her reservation price,she will burn the painting.There are two bidders.The dealer believes that each bidder's willingness to pay will take one of the three following values: $80,000,$70,000,and $45,000.The dealer believes that each bidder has a probability of 1/3 of having each of these three values.The probability distribution of each buyer's value is independent of that of the other's.Assuming that the two bidders bid rationally and do not collude,the dealer's expected revenue from selling the painting is slightly less than

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