Seems that everyone is discussing monetary systems now. Here is a short presentation of Hayek's view.
Ludwig von Mises Institute
A Free-Market Monetary System
Friedrich A. Hayek
As Hayek admits, there is no legal obstacle in most jurisdictions preventing some enterprising firms from putting his proposal to the test. So far, no takers. What does that say about the idea?
Well, in fairness to Hayek he don't think that it would actually happen absent getting the govt out of money creation, because bankers can do very well under the present system and have no incentive to innovate. My response would be whether ending govt money creation and going to a private standard that would only emerge later after testing in marketplace could be managed with smooth transition. And even if it could, it there any actual evidence that it would work?