Why I Study ... Auction Theory

Associate Professor of Mathematics Will Gryc shares how a workshop got him interested in this real-world-applicable discipline.

By: Will Gryc, as told to Meghan Kita  Thursday, March 4, 2021 01:57 PM

I was trained in something called Yang–Mills theory—that was the subject of my Ph.D. thesis. When I started teaching, I wanted to have something I could work with undergraduates on, and Yang–Mills theory was not that subject. It took me into my third year of graduate school to even understand the question I was trying to solve.

In 2008, I had the opportunity to go to a week-long workshop on financial mathematics, and part of the assigned reading was a book about eBay. All my life, I’ve been a collector, and eBay first came on my radar in like 1998. I’ve used it to fuel my collections—old Star Wars toys, baseball and hockey cards. The book talked about applying math not just to eBay but to different types of auctions. The workshop itself dedicated only one day to auction theory, but I was hooked after that.

I read more on my own and started doing projects with students, including one on strategies for making best offers on eBay. We analyzed, in a setting where you have an auction with a Buy It Now price and an option to make an offer, how should a bidder behave? Should they submit an offer or choose Buy It Now? If they make an offer, how big of an offer should they submit?

This is more complicated than a regular eBay auction, where you just bid your value. I have to balance the surplus I would get if I won a valuable item with a lower bid against the possibility that I wouldn’t get the item because I bid too low. Mathematically, we analyzed: Where’s that equilibrium point? We presented our results at a conference in California, and later, we published our results in a journal.

Auction theory is interesting to study because auctions are more ubiquitous than you might think. A lot of big, important transactions—like buying a house or car—involve some kind of negotiation, where the price is not really fixed or it’s not clear what an item’s price should be. Having a good understanding of auction theory can help you navigate those situations as a consumer.