Asymptotic Evolution of Ideal Money

It seems possible and not unlikely, however, that if two states evolve towards having currencies of more stable value as measured locally by national CPI indices that then also these distinct currencies would tend to evolve towards more stable comparative relations of value.
Then the limiting or “asymptotic” result of such an evolutionary trend would be in effect “ideal money” but this as a result achieved without the adoption of anything like an ICPI index as a basis for the standard of value. Nash, Ideal Money

I am thinking of this statement in relation to the emergence of bitcoin and ethereum (and in regard to the relevance of b-money).

(edit: this could be thinking in the wrong direction, but it seems that even if these value trends were not perfectly stable (or asymptotically) there still might be this effect if they are the most optimally valuated currencies in this regard.)

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