Mathematics of the Internet E-Auctions and Markets

Not since AD 193, when the Roman empire was auctioned to the highest bidder has there been so much interest in auctions. The internet has done that. Many dot-coms have recently been established to facilitate transactions such as auctions, procurement, and bidding over the internet. Established "old-economy" companies have responded with a variety of marketplaces of their own, some of which involve joint-ventures between long-standing competitors. By having their store front on the internet, these market place can connect any buyer to any seller, offer products and services for sale in unprecedented variety and quantity. Business Week recently estimated that there may be as many as 600 companies that have been set up to connect buyers to sellers. They connect business to business, and business to sellers, providing a new, immense infrastructure for transactions.

While bidding and auction theory is a mature topic in economics, internet auctions and new markets offer the opportunity to put theory into practice as well as push the theory in new directions. For example,auctions where bidders care not only about what they get but what others get as well. Auctions where bidders care about price as well as other features like quality or reliability. Moving away from auctions to markets in general, there is the issue of price setting in markets involving indivisibilties of various kinds. For example, how does one match and execute buy offers that are contingent upon the execution of another different sell offer? Implementing auctions and markets with theoretically desirable properties sometimes raises thorny computational issues. How are these to be resolved?

Much of the existing literature on auctions restricts attention to the case where a single object is for sale. The internet provides new possibilities for using new auction formats and bidding mechanisms where multiple objects are sold simultaneously.

Mathematical topics arising from this area of research includes optimization, game theory, combinatorics, partial differential equations and simulation.

The three-day IMA workshop is intended to bring together leading researchers in economic theory of markets and auctions with applied mathematicians to discuss research in e-auction and markets. It is meant to encourage new collaborations that address these problems of significant intellectual and economic value. The workshop will include a set of overview lectures accessible to applied mathematicians, complemented by more technical talks on specific topics which emphasize the mathematical challenges posed by these problems.