I stumbled upon this talk by David Friedman about how you could construct a society with no government. You could call it anarchy, but Friedman seems to call it “radical capitalism”. He wrote a book named “The Machinery of Freedom”, and this talk is based on that. Fullscreen is recommended.
There are more details about the economics of it in The Market for Law (video link doesn’t work, so go for the audio), including the weaker sides of such a system. For example environmental protection is problematic.