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20? ? ?? ? ?win lo s eSecondPrice, SealedBid Auction ?Expected gain to bidder 1 is ?How is this maximized? ?If v1 b2, then maximize the prob. of winning。 . set b1 = v1. ?If v1 b2, then minimize the prob. of winning。 . set b1 = v1. ?Either way, telling the truth is best! ( ) P r ( ).v b b b1 2 1 2? ?SecondPrice, SealedBid Auction ?Since truthtelling is best for every bidder, the highest valuation bidder will win. ?Hence the secondprice, sealedbid auction is Paretoefficient. CommonValue Auctions ?The item for sale has the same value to every potential buyer. ?Potential buyers differ in their own estimates of this mon value. ?Bidder i’s estimate is where is the mon value and is bidder i’s estimation error. v vi i? ? ?v ?iCommonValue Auctions ?Bidder i’s estimate is where is the mon value and is bidder i’s estimation error. ?If every bid is truthful, the winner is the bidder with the largest estimation error ?so a truthful winner on average pays more than the true value the winner’s curse. v vi i? ? ?v ?i?ivSummary ?Why auction? ?Efficiency and revenue criteria of auction design ?The Vickry Auction ?Common value auctio