With all this fuss around "In Rainbows", and discussion of whether this is going to revolutionize the music industry, no one seems to have mentioned that there is an entire industry that has been running on essentially the same principal for decades.
Public Radio in the US (think Radio 4, only twee in an entirely different set of ways) basically operates in exactly the same way: it gives its wares away from free (broadcast radio), and requests the listener to make a donation. Since there's no necessity to comply, they perforce request 'whatever you think is appropriate', although they are keen to give suggestions as to what is appropriate ($10 per month, or 'just a dollar per day' are common examples). The model is a little different in places: since the good is a continuous stream, rather than an album, they periodically interrupt this stream to beg for money. Sometimes for days at a time. Moreover, the game theoretic aspect is slightly altered, since there is a greater incentive to contribute to NPR: fail to donate, and the service might go away, or at least become less usable (more begging, less content). Probably you can argue the same about Radiohead albums, although it's more discrete, and there are more competitors than there are for speech-based radio stations not broadcasting insane rants.