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Science
ANOTHER 5 NUMBERS: Game Theory
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Simon Singh investigates another five very important numbers.
Friday 31 October 2003 3.45-4.00pm
Mobile money
Listen again  Listen again to Programme 5: Game Theory

Not long ago auctions seemed to be the preserve of either the mega-rich, bidding for Van Goghs at some plush auction house, or the shady car-dealer, paying cash-no-questions-asked for vehicles of dubious provenance. However, the advent of the Internet and David Dickinson has changed this. Auction web-sites allow the average punter to buy and sell pretty much anything, whilst an army of Bargain Hunt devotees can now happily tell their Delft from their Dresden.

But this auctioneering is just the tip of the iceberg. In 2000, the UK government received a windfall of around £23 billion from its auction of third generation (3G) mobile phone licences. This astronomical sum wasn't the result of corporate bidders "losing their heads", but a careful strategy designed to maximise proceeds for the Treasury.


Its architect was Professor Ken Binmore of University College London. He devised an auction, seeped in a branch of mathematics called game theory. Game theory deals with player's tactics. In any given game, a participant develops a strategy that incorporates their own strengths and goals, and those perceived in their opponent(s). Incomplete information and "bluff" can make things more complicated, and the balance shifts from a purely mathematical approach to one involving greater psychology. But game theory doesn't just apply to cards and Tiddlywinks. In the 1950s, mathematicians started to use these principles to study the economy. One such proponent was Princeton University's John Nash. Immortalised by an Oscar-winning Russell Crowe in the film 'A Beautiful Mind', Nash helped revolutionize game theory with the 'Nash equilibrium'.

Nash focussed on 'non-zero sum' games. These occur when all sides can win or lose, unlike traditional 'zero-sum' games like poker, where one person's victory simultaneously heralds the opponent's defeat. 'Nash equilibrium' occurs when competing strategies achieve a win-win compromise. All participants realise that the end result might not be in their best individual interest, but collectively it suits all. Applied to the real world, many economic transactions fall into the 'non-zero sum' category.


The practical application of these principles came into their own for the UK 3G licence auction. Binmore's remit was to devise a mechanism that would leverage the government's goals of maximising income and encouraging new blood into the industry. Traditionally, such licences had been tendered arbitrarily, based on intuitive rather than mathematical considerations. This meant low revenues, and licences going to the wrong companies.

Binmore's application of game theory ensured this didn't happen. He devised an auction with game rules engineered to achieve the government's objectives, but which would also generate a 'Nash equilibrium' or win-win for all. Critics have argued that the phone companies paid over the odds but Binmore is more circumspect, arguing that they paid what they knew they could recoup from future profits.

In the case of mobile phones, game theory has proved a big win for the government. But for the rest of us, it just means more annoying ring tones on the bus journey home.


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