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In _Denationalisation of Money_, Hayek supposed that competing private fiat-like monies would vie for market share by demonstrating their stable purchasing power. But, as I observed many years ago, Hayek overlooked something of fundamental importance. https://twitter.com/GeorgeSelgin/status/1390339358125928451
He assumed that private individuals, in deciding which monies to prefer, would judge them by their _macroeconomic_ merits. In that case, the macroeconomically best would win. Hayek assumed this would mean those with the most stable purchasing power.
Granting Hayek's assumption for the sake of argument, his conclusion was a non-sequitur. In choosing what money to prefer, why would people act differently than they do in choosing other goods or assets? Why not pick the fiat-like money promising the greatest _private_ gains?
That could mean preferring not stable purchasing-power products but ones that could appreciate. And of course, if enough did so, the expected appreciation would become a self-fulfilling prophesy, with consequences quite unlike those predicted by Hayek's theory.
First, if the chosen product did indeed become "money," that is, the dominant medium of exchange and unit of account, it would bring deflation, and possibly very severe deflation--a potentially serious problem in the presence of downward nominal price and wage-rate rigidities.
But the second and more fundamental problem was that, precisely because it offered such high returns, the chosen medium would be held (or, in today's vernacular, HODLed), rather than routinely exchanged for goods and services.
That is, the very qualities that made it more popular that rival products would also prevent it from every becoming "money," meaning a widely-used medium of exchange and account. Instead, it would serve only or overwhelmingly as a pure "store of value" or investment medium.
Nor are these the only problems with Hayek's theory. As @lawrencehwhite1 and others have shown, even if an issuer of a stable purchasing power "private fiat money" succeeded in gaining a large market share, it might then profit by breaking its promise and issuing oodles of it.
It's partly for this reason that monies freely convertible into commodities "won out" in historic currency competitions.
Whether any modern cryptocurrency can succeed in overcoming these problems remains to be seen.
