Over a rabelaisian feast with convivial company, conversation turned to a twitter contretemps between economic theorists known to us at table. Its proximate cause was the design of the incentive auction for radio spectrum. The curious can dig around on twitter for the cut and thrust. A summary of the salient economic issues might be helpful for those following the matter.

Three years ago, in the cruelest of months, the FCC conducted an auction to reallocate radio spectrum. It had a procurement phase in which spectrum would be purchased from current holders and a second phase in which it was resold to others. The goal was to shift spectrum, where appropriate, from current holders to others who might use this scarce resource more efficiently.

It is the procurement phase that concerns us. The precise details of the auction in this phase will not matter. Its design is rooted in Ausubel’s clinching auction by way of Bikhchandani et al (2011) culminating in Milgrom and Segal (2019).

The pricing rule of the procurement auction was chosen under the assumption that each seller owned a single license. If invalid, it allows a seller with multiple licenses to engage in what is known as supply reduction to push up the price. Even if each seller initially owned a single license, a subset of sellers could benefit from merging their assets and coordinating their bids (or an outsider could come in and aggregate some sellers prior to the auction). A recent paper by my colleagues Doraszelski, Seim, Sinkinson and Wang offers estimates of how much sellers might have gained from strategic supply reduction.

Was the choice of price rule a design flaw? I say, compared to what? How about the VCG mechanism? It would award a seller owning multiple licenses the marginal product associated with their set of licenses. In general, if the assets held by sellers are substitutes for each other, the marginal product of a set will exceed the sum of the marginal products of its individual elements. Thus, the VCG auction would have left the seller with higher surplus than they would have obtained under the procurement auction assuming no supply reduction. As noted in Paul Milgrom’s  book, when goods are substitutes, the VCG auction creates an incentive for mergers. This is formalized in Sher (2010). The pricing rule of the procurement auction could be modified to account for multiple ownership (see Bikhchandani et al (2011)) but it would have the same qualitative effect. A seller would earn a higher surplus than they would have obtained under the procurement auction assuming no supply reduction. A second point of comparison would be to an auction that was explicitly designed to discourage mergers of this kind. If memory serves, this reduces the auction to a posted price mechanism.

Was there anything that could have been done to discourage  mergers? The auction did have reserve prices, so an upper limit was set on how much would be paid for licenses. Legal action is a possibility but its not clear whether that could have been pursued without delaying the auction.

Stepping back, one might ask a more basic question: should the reallocation of spectrum have been done by auction? Why not follow Coase and let the market sort it out? The orthodox answer is no because of hold-up and transaction costs. However, as Thomas Hazlett has argued, there are transaction costs on the auction side as well.