The meaning of the word "stabilize" isn't clear from the article, despite being used 12 times in the body and once in the title.
It would have been easy to make the article more clear. Simply explain what aspect of Bitcoin is supposed to stabilize.
Given the unending fascination with the USD/BTC exchange rate, it can be assumed that the author is referring to this metric. The inclusion of the heading "Does the price of Bitcoin have a Nash equilibrium?" also supports this idea.
However, if this is the case, why does the author include the following quote the middle of the article:
Why has Amazon stabilized, and will bitcoin do the same? When Amazon shares debuted back in 1997, earnings were non-existent. […]
So the article concludes that Bitcoin can gain stability by being anchored to the price of gold. However isn't gold a "Keynesian Beauty Contest"? That is, gold is valuable because other people believe other people believe it is a store of value.
Bitcoin doesn't need to stabilize to be successful. In the same way that the exchange rate of the hyperinflating German Mark and gold didn't need to stabilize. All bitcoin needs to do is continue to operate with it's programmed monetary policy such that its value can't be inflated away through coercion.
Money is a commodity whose goal is to transport value through space and time. We are living through -- in human-species scale -- a brief 90-year experiment in the artificial elimination of a free market of monies by violence of the state (until bitcoin was invented).
Artificially increasing and decreasing the supply of money in an economy has about just as much utility as artificially increasing and decreasing the supply of any other good -- which is none.
Bitcoin's success narrative doesn't depend on the amount of non-scarce dollars the market is willing to trade for it ceasing to change ('stabilize'). The success narrative is: an increasing set of people understanding that the hardest money always wins. Bitcoin is one halvening away from being harder than gold and is _the_ hardest money ever in existance. Those who have taken exposure to bitcoin will have more wealth preserved than those who denominate their value in inflatable dollars. As more people see bitcoin improving the quality of life of individuals they also take exposure to bitcoin. This process doesn't need a planner nor intelligent agents, it just needs bricolage.