
The Denationalisation of Money is a 1976 book by Friedrich Hayek. The author advocated the establishment of competitively issued private moneys. In 1978 Hayek published a revised and enlarged edition entitled Denationalisation of Money: The Argument Refined, where he speculated that rather than entertaining an unmanageable number of currencies, markets would converge on one or only a limited number of monetary standards, on which institutions would base the issue of their notes.
Equally interesting and probably easier to believe are gold backed currencies with competing private institutes issuing goldbacked money.
Still, its great to see people thinking about money in another way than just how to get it.
The most influential statement of your proposal is Hayek's article "Choice in Currency: A Way To Stop Inflation"[1] which he later expanded on in "Denationalisation of Money".
Hayek's views have an admirable internal consistency, but his political premises are contrary to the core values of almost every pre-industrial society, and of the social democratic tradition in Europe which has been internationally influential.
Very few people understand the full scope of Hayek's political vision, which is premised on a thoroughgoing skepticism toward the very possibility of rational democratic deliberation. If they fully understood his proposal's implications, I doubt they'd support them; but certainly there are some who are willing to fully own their anti-democratic implications.
1: https://iea.org.uk/publications/research/choice-in-currency-...
Perhaps most relevantly he wrote a book on the idea of competing private currencies (Denationalisation of Money -- it seemed meant for people with more knowledge of economics or finance than me).
With the banks we're used to there's a potential tragedy of the commons in that their separate decisions all affect the shared money supply, which is indistinguishable, so one reason to have a central bank is to get some overall control of those distributed decisions. A distinct competing currency already under a single decision maker doesn't so obviously need that extra governance. I don't know, maybe it does, but I'd like to see the reason spelled out.
(Hayek raised this point in his Denationalisation of Money.)
> Gresham's Law will apply only to different kinds of money between which a fixed rate of exchange is enforced by law
(Emphasis in the original)