Paul Milgrom today delivered the annual Nomura lecture at the Mathematics Institute at Oxford University in the UK. The annual lecture highlights applications of mathematics in a variety of different fields. This year’s lecture, entitled “Strategy-Proof Auctions for Complex Resource Allocations,” was delivered to a large audience of mathematicians and others in the Martin Wood theatre in Oxford.
In substance, the lecture described the special challenges facing US regulators in designing an auctions to buy back television broadcast licenses. The intention is to clear free the spectrum to be used for future wireless broadband networks. But this particular auction problem involves unprecedented challenges, because evaluating any given set of bids for broadcast stations to go off-air requires creating a plan to reorganizing the remaining on-air broadcasters, and that problem is computationally challenging even for the fastest modern computers. Building an auction in which different combinations of bids needs to be evaluated is even harder, since it requires evaluating many such plans. Milgrom described plans that his consulting team at Auctionomics have developed and recommended to regulators and also reported mathematical theorems that he and his Stanford colleague Ilya Segal developed to characterize the properties of the recommended auction.
The ability to handle complex constraints like these in an auction, which is a true market mechanism, is not only novel, but also has a wide range of potential applications. For example, auctions to add capacity to networks or to allocate limited airspace for satellite launches and air transportation are similarly complex and may be manageable by similar methods.