Modeling Opportunities in Auctions

This paper argues that the answers to interesting questions about real auctions depend, often critically, on the particular mathematical assumptions that go into a model of an auction situation. It then suggests some understudied areas for fruitful mathematical research on competitive bidding. These include asymmetry, financially constrained bidders, complicated information structures, bidder decisions about auction participation, the effect of repeated auctions involving the same participants, auctioning items with interrelated values, and transaction costs. The paper also discusses two major areas where new, complicated auctions are being designed—combinatorial spectrum auctions and electricity and transmission rights auctions. Acknowledgements and Disclaimer. This paper is based upon a presentation to the IMA Workshop on “Mathematics of the Internet: E-Auctions and Markets” on December 3, 2000. Over the years, I have benefited from discussions with bidders, those conducting auctions and most of the smart people who have worked on bidding theory. I have also been supported, in part, by Shell, Xerox, DOE, Rutgers, and several NSF grants. However, the idiosyncratic opinions expressed here are solely my own and should not be attributed to any organization or individual with which I have worked or who was kind enough to give me information or financial support.