Auctions have been around for centuries and the mathematical analysis of auctions dates back decades. But they have enjoyed growing popularity in recent years because the Internet has made efficient implementation of auctions, even complex ones, possible. Consumer auctions like eBay have become household names, but business‐to‐business (B2B) auctions have grown even more quickly. B2B auctions are mainly procurement auctions in which there is a single buyer and multiple sellers (the reverse of most consumer auctions; in fact, such auctions are called reverse auctions). For example, auto manufacturers have set up auctions in which thousands of potential suppliers bid for contracts; the auto company chooses the suppliers with the lowest prices. Clearly, such an undertaking would be much more cumbersome without the Internet. We will consider auctions with a single seller and multiple potential buyers.
There are many types of auctions, each with various properties in terms of consumer behavior, efficiency, and so on. Here are just a few types of auctions that have been introduced in the literature and in practice:
- English: Perhaps the most familiar type, with each bidder publicly announcing his bid and the price rising until only a single bidder remains. The highest bidder wins and pays his bid.
- Sealed‐bid first price: Bids are made privately and simultaneously by all bidders. The bidder with the highest bid wins and pays his bid.