Why you should bid your true value in a second-price auction
An item is sold by sealed bids. Everyone submits one bid; the highest bidder wins but pays the second-highest bid. The item is worth exactly V to you, meaning you are happy to pay anything below V and unhappy to pay anything above it. You know nothing about the other bidders.
What should you bid? Prove that your recommended bid is at least as good as any other bid, whatever the other bidders do.
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Compare bidding V with bidding some higher number H and with some lower number L. In each comparison, split into cases according to where the highest competing bid falls.
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