Verifying algorithms

The Smith Institute designed scenarios to test the implementations of Ofcom’s spectrum auction rules and verify correct operation.

The problem

Ofcom’s duty under the Communications Act 2003 to further the interests of consumers, where appropriate by promoting competition, is of particular importance to its current series of spectrum awards. In fulfilling this duty, Ofcom aims to secure optimal use of spectrum, to promote innovation in technology and services, and to secure the availability of telecommunications services to consumers.

In 2008, Ofcom broke new ground by instigating the use of combinatorial clock auctions as a mechanism for the effective allocation of radio spectrum. The first two frequency bands to be awarded using this auction design were:

  • 10-40GHz: February 2008
  • 1452-1492MHz: April/May 2008

Followed by:

  • Combined 800MHz & 2.6GHz: January/February 2013

There are several important advantages over alternative designs. Bidders who wish to assemble packages of spectrum licences avoid exposure to the risk of being left with only a partial package; there are natural incentives to adopt bidding strategies that reflect true valuations; and the design discourages attempts at collusive bidding strategies.

The high value nature of spectrum auctions determined the need to verify the accuracy of the software to be used by Ofcom to run the auction. Therefore the requirement for an independent company to conduct the verification of the auction results software rose prominently and as a result Ofcom engaged in 2007 the Smith Institute in the awards process.

The solution

The Smith Institute has advised Ofcom on the implementation of the awards at 10-40GHz, 1452-1492MHz and 800MHz&2.6GHz. In each case, the auction design is underpinned by detailed mathematical algorithms to determine the winning bidders and the prices that they pay. We have assessed for correctness the software implementations of these algorithms, basing our analysis on the rules and regulations of the individual awards. We have undertaken a series of independent systematic assessments of the proposed software implementations, using suites of carefully designed test cases to reflect the possible auction scenarios.

Through these investigations we have been able to reach an informed independent opinion on whether Ofcom can have confidence that the auction results software is working correctly, and have been able to make recommendations for modifications where appropriate. Throughout this work, we have worked closely with Ofcom’s Spectrum Policy Group and other Ofcom suppliers.

In particular, for the combined 800MHz & 2.6GHz spectrum award, the Smith Institute provided an independent verification of the correctness of the results produced by the Auction Engine during the live auction and prepared a report on correctness of the final results for Ofcom to publish on its

A report on correctness for the outcome of a combinatorial auction provides a mathematical proof that the result is correct. In addition to providing a guarantee of correctness, it also allows interested parties to carry out their own verification after the event.

The benefit

Through its detailed understanding of the UK spectrum auction regulations and of the underpinning mathematics, the Smith Institute provided independent verification of the performance of Ofcom’s auction results software to Ofcom’s Spectrum Policy Group.

Additional information

The Smith Institute has provided Q&As on the design and outcome of the Ofcom 4G Auction.

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