How can governments apply the principles of game theory to devise a spectrum auction which maximises revenue?

An auction is a game. All good players must strive to get as much of a scarce resource, for as little as possible, while the seller aims to maximise their revenue. To play well, you must play ‘a game within a game’ so to speak; applying the principles of ‘game theory’. A game, to a game theorist, is any activity in which your prediction of what another person will do affects what you decide to do and is evident in many activities involving human interaction, the most obvious being poker. Poker is full of spirals of secrets, second guessing and bluffs; a game not just of luck, but skill too as you attempt to outwit your opponents, just like an auction. Is a small bet a sign of weakness, or a trick to lure you into raising the stakes against hidden strengths? And just like an auction, a monetary stake is central to play as bets act as a form of communication to the other players. In the case of a spectrum auction, the stakes are incredibly high indeed and game theory is key to determining the outcome. The multibillion pound question is: how can governments apply the principles of game theory to devise an auction which maximises revenue?

A spectrum auction is a process whereby a government uses an auction system to sell the rights (licences) to transmit signals over specific bands of the electromagnetic spectrum with the ultimate goals of efficiently allocating scarce spectrum resources to the parties which value them the most, while securing revenue in the process. However these auctions do not always go to plan, as experienced most costly by the US who raised less than 1% of the expected revenue in a 3G auction. Despite this, the UK made the bold step to auction off five licences for radio spectrum for ‘third generation’ (3G) mobile telephone services in 2000. Determined not to face a similar fate to the US, the British government employed a team of game theorists to design an auction, with the benefit of hindsight from the US auction, which would maximise revenue for the government while ultimately preventing them from becoming a laughing stock. The auction was a phenomenon, raising ten times the revenue which was expected. A blessing for game theory, but how was it possible?

The US government employed game theorists to sell spectrum rights in the late 1990’s, no simple task when companies could bid for licenses for various regions throughout the US. It was cheaper for companies to run adjacent networks in different areas, however how do they know the value of the rights for one area when they have no guarantee to win the rights in another area? To overcome this complex problem the theorists designed a complex set of parallel auctions. The first flaw major flaw which the UK theorists duly noted; complexities cause collusion. Bids for the rights were rounded to the nearest few thousand dollars and therefore firms were able to signal which licenses they’d prefer by containing geographical area codes in their bids. Through this communication they could avoid aggressively bidding against each other as there was no competition for the rights, a vital factor in demand and supply. The US government was like a poker player oblivious to the other players winning all his money through a series of secret nods and winks.

As a result the British game theorists organised the sale of the 3G spectrum rights in the UK as a simultaneous ascending auction. The key features of a simultaneous ascending auction are that all licences are sold simultaneously, there are multiple rounds, new bids can be made in each round and the auction closes only when bidding on all licences has stopped. This method was totally transparent with each of the rounds being posted on the internet; the auction was to take place in full view of the world. In addition to the transparency, the restriction to acquire just one license unlike in the US prevented collusive strategies from humiliating game theory once again.

The US auction proved that transparency was essential. In the UK, every bid and the identity of the corresponding bidder were made public after each round. This was true not just for the currently leading bids for each licence but also for all losing bids. Therefore bidders were learning from each other’s bids about what the 3G licenses were likely to be worth, creating a shared confidence that the licenses would prove hugely valuable. An alternative may have been to run a ‘sealed-bid’ auction whereby everyone handed in an envelope containing a single bid however this could have led to bidders guessing in the dark, leading to much more conservative bidding and a much less profitable outcome for the government.

Furthermore the simplicity of this format may explain why so many companies decided to bid, with a total of 13 serious bidders who each had to commit an initial £50 million deposit. Each bidder was able to make a judgement of how much they valued the licenses they were bidding for, based on factors including how innovative their ideas were, the capital they owned and their sales expectations. Therefore nobody is in a position to lie. Talk is cheap, but bidding is expensive. This transparent auction system forces each bidder to tell the truth about his own estimate of the license’s value while the auction broadcasts the collective view to all bidders, so that they can update their own opinions accordingly.

To conclude, the UK spectrum auction is a perfect example for clearly demonstrating how game theory can be used with miraculous effects, raising a total of £22.5 billion for the UK government which is enough to halve the basic rate of income tax for a year, becoming the biggest auction in modern history. Game theory proves that a simple and transparent auction such as the simultaneous ascending auction neatly summarises the collective wisdom of all the bidders while avoiding collusive strategies which proved fatal in the US auction.

Contributed by Sam Timmins

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