Auctions

Suppose two bidders are bidding for a painting that each knows is worth between $100,000 and $500,000, and that each bidder's valuation of the painting is uniformly distributed between $100,000 and $500,000. Each bidder submits a sealed bit.

If bidder 1's true valuation is $200,000, then she bids $150,000, and if bidder 2's true valuation is $250,000, then bidder 2 bids $175,000. The auctioneer in this case collects $175,000 and bidder 2 gets the painting for $175,000.

If instead the auction is an English auction the bidding would stop as soon as the bid went over $200,000. Thus, the auctioneer will net a little over $200,000 for the item. In the case of the sealed-bid auction, where the beliefs of the bidders about the valuations of the others are uniformly distributed between $100,000 and $500,000, the winning bid is only $175,000. Thus, in this case, the English auction generates significantly more revenue for the auctioneer than the sealed-bid auction.

In contrast, if the valuations of the bidders are uniformly distributed over $200,000 and $500,000 and bidder 1's true valuation is $300,000 and bidder 2's valuation is $200,000, the the sealed-bid auction would get a winning bid of $250,000 and the English auction could get a winning bid of only $200,000. Thus, in this case the sealed-bid auction generates substantially more revenue than the English auction.


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