Rod's Auction House holds sealed-bid auctions for used computers every Tuesday. Each used computer is sold to the highest bidder at the second-highest bidder's bid. On average, half of the computers sold at Rod's Auction House are lemons, and half are good, used computers. A good, used computer is worth $750 to any buyer, and a lemon is worth only $200. Buyers are allowed to look over the used computers for a few minutes before they are auctioned. Almost all the buyers who attend the auction can do no better than random choice at picking good computers from among the lemons. The only exception is Al. Al can sometimes, but not always, detect a lemon by touching the tower and feeling its vibrations. The vibrations generated by a good computer's tower are always very regular and soft. On the other hand, the tower of 1/3 of the lemons emits very irregular and strong vibrations, while the tower of the remaining 2/3 of the lemons emits vibrations that are no different from those of a good computer. Al attends every auction and touches every tower. Taking into account the results of his test, he bids his expected value for the computer. Question*** Suppose that bidders other than Al believe that they will only get a computer whose tower emits strong and irregular vibrations, and suppose that they bid their expected value for such a computer. Suppose also that, for every computer, Al bids his expected value, given the results of his touch test. What is Al's expected profit on a computer that passes his test? (Remember that computers are sold to the highest bidder at the second-lowest bid.)
Rod's Auction House holds sealed-bid auctions for used computers every Tuesday. Each used computer is sold to the highest bidder at the second-highest bidder's bid. On average, half of the computers sold at Rod's Auction House are lemons, and half are good, used computers. A good, used computer is worth $750 to any buyer, and a lemon is worth only $200.
Buyers are allowed to look over the used computers for a few minutes before they are auctioned. Almost all the buyers who attend the auction can do no better than random choice at picking good computers from among the lemons. The only exception is Al. Al can sometimes, but not always, detect a lemon by touching the tower and feeling its vibrations. The vibrations generated by a good computer's tower are always very regular and soft. On the other hand, the tower of 1/3 of the lemons emits very irregular and strong vibrations, while the tower of the remaining 2/3 of the lemons emits vibrations that are no different from those of a good computer. Al attends every auction and touches every tower. Taking into account the results of his test, he bids his expected value for the computer.
Question***
Suppose that bidders other than Al believe that they will only get a computer whose tower emits strong and irregular vibrations, and suppose that they bid their expected value for such a computer. Suppose also that, for every computer, Al bids his expected value, given the results of his touch test. What is Al's expected profit on a computer that passes his test? (Remember that computers are sold to the highest bidder at the second-lowest bid.) $
Step by step
Solved in 3 steps
