Myerson's Lemma

Myerson's Lemma is a principle in auction theory that helps design optimal auctions. It states that the expected revenue from an auction can be found by integrating the item's virtual valuation—an adjusted version of the bidder's true value—over the range of possible bids. Essentially, it transforms the problem of maximizing revenue into analyzing these virtual values, allowing sellers to set reserve prices and allocation rules that maximize expected profit. This lemma provides a mathematical foundation for creating auctions that are efficient, fair, and revenue-maximizing by focusing on bidders' true valuations and their virtual counterparts.