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Developer Eidos is offering a download of the game from a penny, along with a £2.50 transaction fee.
It is the first time that a pay-what- you-want model has been tried with video games, said the developer.
UK rock band Radiohead used a similar sales strategy in 2007 with its album In Rainbows.
A survey found that nearly two-thirds of downloaders paid nothing for the album.
The new game will be available to download until 10 September, when the price will rise to £29.99.
Additional content for the game will be sold throughout the year, costing £5 for six updates.
"This is the first time an initiative like this has ever been tried in the videogames market," said Roy Meredith of Eidos.
Source: BBC