It looks like Finland will be the first to attempt this idea.
http://www.basicincome.org/news/2015/12/finland-basic-income-experiment-what-we-know/
I think it will just cause rice increases in basics like rent, heat\power, and food. Since the locals know everyone has more money, the price to live there should naturally rise. It will be interesting to watch what happens.
Finland will be a great experiment for it. I'm not sold on Basic Income at all, but technological change is going to put so many people out of work that we'll need to come up with something. Either the government provides some benefit like this or else we need a full-scale economic transformation. Those people who cannot work can certainly work in the P2P economy and/or start their own businesses, but not everybody has those skills or opportunities. I doubt that huge corporations and wealthy individuals are going to willingly give back a big chunk of the economy to small-scale entrepreneurs. But maybe they will if there's no one who can afford to buy their products and services.
As a Finn, I'm quite pessimistic on this. The experiment will be probably too short to draw any conclusions and it's not going to be full basic income. It will only replace some of the current welfare subsidies. Most of our politicians are really, really stupid (as they are all around the world) so they will probably fuck up this.
The price of living is already very high, thanks for massive taxation and regulation. Especially rents are high, partly because landlords know that current welfare system pays the rent up to a certain amount. Of course rents usually don't go below that amount.