# Ofcom 4G Spectrum Auction Q&As

The recent auction for 4G spectrum licences was the highest profile example of a combinatorial auction ever held in the UK.  The Smith Institute for Industrial Mathematics and System Engineering worked alongside Ofcom to ensure the smooth running of the auction process.  The auction systems relied on a suite of mathematical algorithms for the determination of winners and prices.  The Smith Institute's role involved testing the auction systems and independent verification of the live auction results.  Drawing on this experience of close involvement with the auction process, the Smith Institute has produced the following summary of the auction and its outcome.

## How are the winners determined?

The 4G auction is a combinatorial auction, meaning that each bid is for a 'package' of spectrum lots together with a bid amount.  Each bidder submits a collection of bids, through the various rounds of the auction, but at most one bid per bidder can be part of the winning combination. The winning combination of bids is the one with the highest total of bid amounts, subject to the available supply of spectrum and some special conditions.

## What special conditions?

When calculating the total bid amount from a combination of bids, any unsold lots are included at their reserve price.  This condition did not affect the winning combination of bids, but did influence the prices paid.  To be valid, a combination of bids must also meet the requirement that a fourth national operator (in addition to Vodafone, Everything Everywhere and Telefonica) be awarded a certain minimum set of lots.  Hutchison 3G was the operator that benefited from this condition.

## How are the prices determined?

Prices are determined on a second-price basis.  If just a single lot were auctioned, then the highest bidder would pay the amount of the second highest bid.  In a combinatorial auction, such as the 4G auction, the corresponding requirement is that winning bidders pay just sufficient that others are not prepared to pay more, as expressed by their bids.  The prices paid by each winning bidder are at least the reserve prices for their winning packages and at most the bid amounts of their winning bids.

## What were the auction’s objectives?

The primary objective of the auction was to maximise the future benefits to consumers of mobile services.  This has two aspects: ensuring that there are four national operators, to maintain a competitive mobile market, and awarding spectrum licences to those operators who are able to make the most effective use of them.  Maximising the return to the Treasury is not part of the objectives of the auction design.

## Where can I find out more about the auction rules and design?

There are two key documents: the Information Memorandum [1] and a subsequent update [2], and the auction Regulations [3], [4], both of which are available on the Ofcom web site.  The Regulations document is the statutory instrument that sets out the complete auction rules.

## Who won spectrum and who didn't?

Seven companies participated in the auction: the four existing mobile operators, Vodafone, Telefonica, Hutchison 3G and Everything Everywhere, alongside HKT, MLL Telecom and Niche Spectrum Ventures.  Five of the seven were successful in securing new spectrum licences, covering 250MHz of spectrum in total, in bands at 800MHz and 2.6GHz.  The unsuccessful bidders were HKT and MLL Telecom.  Ofcom has published the full auction data, including the detailed bidding histories [5].

## Why weren’t winning bidders asked to pay the full amounts of their bids?

The usefulness of different packages of spectrum to each bidder is indicated by the amount of their bids.  To ensure that spectrum is efficiently allocated to those bidders who attach the highest value to it, bid amounts must be an honest reflection of the bidders’ valuations.   If bidders were asked to pay the full amounts of their winning bids, they would have strong incentives to bid below their true valuations (called 'shading').  Different bidders may shade their bids by different amounts, resulting in an inefficient allocation.  The second-price rule largely eliminates incentives to shade bids.

## What were the levels of competition in the auction?

To ensure a competitive wholesale and retail market for 4G services, bidders were restricted in the amount of spectrum that they could win.  Coupled to the requirement to ensure four national wholesalers, this may have somewhat reduced the level of competition in the auction, or changed the nature of competition, but offers a better deal for consumers in terms of greater choice and better services.

## Did the reserve prices affect the outcome?

All available spectrum lots were sold in the auction and there is no evidence that the reserve prices were too high. This auction contained a special treatment of reserve prices, which in effect applied them incrementally to each individual lot won and not just to complete packages of lots. This feature meant each bidder had to pay at least the reserve price for each lot in a package, such that strong bidders could not win additional lots in larger packages at no extra cost. This increased revenue by £273.5M, with no evidence of any negative impact on the bidding.

## Did bidders follow good strategies?

In general, bidders who are flexible and express their valuations for a range of different packages are likely to fare better.  The numbers of different packages on which each bidder submitted bids are as follows:

 ` Bidder Name` ` Packages bid for` ` Everything Everywhere` ` 48` ` HKT` ` 9` ` Hutchison 3G` ` 17` ` MLL Telecom` ` 9` ` Niche Spectrum Ventures` ` 89` ` Telefonica` ` 11` ` Vodafone` ` 94`

The losing bidders, HKT and MLL telecom submitted a small number of bids due to only having interest in the most inexpensive lots. H3G decided to “opt in” to benefit from the reservation of spectrum for a fourth national wholesaler. As it was the only bidder to do so it was restricted to bidding on packages that were consistent with that outcome. They could nevertheless choose from over 2,200 different packages of lots and decided to bid on 17 of those. Submitting a large number of bids potentially benefits both the submitter and the auctioneer, as losing bids still play a role in determining the prices paid by other bidders.

## Did Hutchison 3G benefit from the requirement that the auction should result in four credible national operators?

Based on the bids actually submitted, Hutchison 3G would have won the same amount of spectrum without this requirement.  However Hutchison 3G would have had to pay more for the spectrum that it won: £384M instead of £225M.

## Could bidders have improved their outcomes with different bid amounts?

If the bids amounts were the bidders’ true valuations for the packages, then any deviation would not have improved the outcome for that bidder. Furthermore, the prices paid by the winning bidders did not depend upon their own bids, so they could not have reduced the amount they had to pay by lowering their bids. It would have been possible for a bidder to increase the price paid by a competitor by increasing their bids for spectrum packages they didn’t win, but only at the risk of winning a package at a price that was higher than the bidder was willing to pay.

## Why did the two losing bidders not win?

Both the losing bidders were attempting to win 2.6GHz individual frequency lots. Under the auction rules, the minimum bid in this category win is for two lots.  For either of the losing bidders to have won two lots would have required a minimum bid of £11,844,000.  The bid of £10,250,000 by HKT was relatively close, but the bid of £1,011,000 by MLL Telecom was well below the necessary amount.  Despite not winning any spectrum licences, both these bidders increased the prices paid by the winning bidders.

[1] The award of 800MHz and 2.6GHz spectrum: Information Memorandum

[2] The award of 800MHz and 2.6GHz spectrum: Information Memorandum Update

[3] The Wireless Telegraphy (Licence Award) Regulations 2012

[4] The Wireless Telegraphy (Licence Award) (Amendment) Regulations 2012

[5] 800MHz and 2.6GHz Combined Award

Robert Leese is Chief Executive of the Smith Institute and leads it Auction Verification team. Robert has a PhD from the University of Durham and is a Fellow of St Catherine's College, Oxford.  Paul Munday is a Senior Consultant Mathematician within the same team.  Paul has a DPhil from the University of Oxford and is a Fellow of the Royal Statistical Society.

## About the Smith Institute’s Auction Verification team

The Smith Institute’s Auction Verification Team consists of six members of technical staff supported by two account managers.  They have supported the preparation, verification, and certification of twelve combinatorial spectrum auctions across eight countries, more than any other team globally.