The Smith Institute provided quality assurance to Innovation, Science and Economic Development Canada’s (ISED or the Department), previously Industry Canada, spectrum awards in the 700MHz and in the 2500MHz frequency bands.
In 2012, ISED commenced the process of awarding radio spectrum in the 700MHz band. Spectrum in this band was formerly used by broadcasters to provide over-the-air television and in Canada was repurposed for mobile broadband services. It is valued by service providers because it carries signals well over long distances and penetrates structures better than higher frequency bands, making it well-suited to delivering next-generation wireless services.
In the 700 MHz auction, the Department auctioned 98 licences covering 7 blocks of spectrum and 14 geographic areas. In parallel with the 700MHz award, ISED prepared for the 2500MHz award: the Department auctioned 318 licences covering 9 blocks of spectrum and 61 geographic areas.
The auction design used for both awards was the Combinatorial Clock Auction (CCA) format. Like any other auction, the CCA format uses supply and demand to arrive at the final price. However, bidders express interest in packages of blocks instead of on an individual basis. This ensures that bidders do not end up with some, but not all, of the blocks they require to support their business case, thereby avoiding the so-called ‘exposure problem’.
ISED established rules to support auction integrity. As part of this process, ISED contracted the Smith Institute to provide third-party auction verification.
The construction of combinatorial auctions is well established. In addition to avoiding the exposure problem, combinatorial auctions have high economic efficiency, meaning that in applications like radio spectrum their outcomes tend to be ultimately good for consumers. They also create strong incentives for bidders to be truthful and consistent in the bids that they place. For bidders, the main task is to decide which packages are of interest and at what valuations, and these decisions depend on being clear about their individual business plans.
ISED made available 98 licences in the 700MHz award and 318 licences for the 2500MHz award. Both auctions had a detailed lot structure to reflect the regional structure of Canada’s telecommunications market. Spectrum blocks relate to a particular ‘lot’ of frequencies but also to a particular geographical region, a service area. In particular, in the 700MHz auction, the 98 licences covered 7 blocks of spectrum (A, B, C, C1, C2, E, F) and 14 geographic areas; whereas in the 2500MHz award, the 318 licences covered 9 blocks of spectrum (A, B, C, D, E, F,G, H, I) and 61 geographic areas.
We believe that the 2500MHz was the largest combinatorial auction ever held, in terms of the number of blocks available, and it also broke new ground in the way bidders express their preferences, to handle such a large number of possibilities.
Depending on the number of blocks and how they can be combined into packages, the Smith Institute developed its independent mathematical approaches to verify the results. The main tasks were identifying winners and prices from what might easily be several thousand bids in total. We created a shadow implementation of the auction system’s winners and prices calculation. This was based around calculating the constraints imposed by the auction rules and solving the resulting optimisation problem using the integer programming solver, Gurobi. In both auctions, the large number of packages and the potentially high number of bidders necessitated an implementation that was computationally efficient as well as being robust to unexpected outcomes. During the project, we developed a set of automated and manual checks on the results, which are founded on the underlying mathematical theory of optimisation problems, and allowed us to be completely certain that the declared results were correct.
Eight Canadian companies won spectrum licences in the 700MHz auction, raising CAD 5.27 billion. Licences covering 302 of 318 available blocks were awarded in the 2500MHz auction to nine companies, raising CAD 755 million.
ISED took many precautions to ensure the auction integrity. In its published FAQs on the 700MHz award, it noted that “the results of the auction were verified by an independent third party — the highly respected Smith Institute, which is a world-leading mathematical consultancy that provides advice to governments and industry on system design and data analysis. They have provided third-party auction verification for spectrum regulators in the UK and Australia.