Optimal bidding in online auctions

Online auctions are arguably one of the most important and distinctly new applications of the Internet. The predominant player in online auctions, eBay, has over 42 million users, and it was the host of over $9.3 billion worth of goods sold just in the year 2001. Using methods from approximate dynamic programming and integer programming, we design algorithms for optimally bidding for a single item in an online auction, and in simultaneous or overlapping multiple online auctions. We report computational evidence using data from eBay's website from 1772 completed auctions for personal digital assistants and from 4208 completed auctions for stamp collections that shows that (a) the optimal dynamic policy outperforms simple but widely used static heuristic rules for a single auction, and (b) a new approach for the multiple auctions problem that uses the value functions of single auctions found by dynamic programming in an integer programming framework produces high-quality solutions fast and reliably.