Auction Theory — Each bidder has a private valuation drawn from the chosen distribution. English: ascending open-bid, winner pays their final bid. Dutch: price descends from a high start; first bidder to accept wins. First-price sealed-bid: all submit one bid secretly; highest bid wins and pays that amount. Vickrey (second-price): highest bidder wins but pays the second-highest bid — truth-telling is the dominant strategy. The Revenue Equivalence Theorem predicts all four yield equal expected revenue under standard conditions.