In an ideal continuous-price auction with independent private values, bidders remain active up to their valuations. Without a reserve, the last remaining bidder wins at the second-highest valuation. With a reserve price , there is no sale if every valuation is below ; otherwise the winner pays the larger of and the second-highest valuation. Strict versus weak inequalities at the reserve have no revenue effect for continuous valuation distributions. This payment rule is distinct from a first-price sealed-bid auction.
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An English auction is a type of auction that is characterized by the open and ascending nature of bidding. In this auction format, potential buyers place progressively higher bids until no one is willing to bid further. Here are some key features of an English auction: 1. **Open Bidding**: Bids are announced openly, allowing all participants to hear the current highest bid.