The Korx of today are not libertarians. They're ruled by a single corporate monopoly. But historically, the Korx were pure capitalists -- far beyond anything attempted on Earth. Completely unregulated. The military, police, schools, and roads were all owned by private entities and leased out to others as services.
Brad, were you reading Neal Stephenson when you came up with the Korx? His book
Snow Crash comes readily to mind. For those who haven't read it, the society that the former U.S. has become in that book gives a good idea of how such a system might have come into being. The choice of hiring Admiral Jim's Navy to protect your gated community's coastline is one of my favorite examples.