Short Answer: Maybe?

The line between true free markets and mixed economies is very hazy. For example, the black market for opium is manipulated and controlled by the Taliban, which can be considered a governmental organization. Even though there aren't any "official" regulations or rules in that market, is this a true free market? Or how cartels, which are non-governmental organziations, can literally kill off their competition, and thereby manipulated the "free" market.

The problem with "true" free market systems right now is that they almost always devolve into oligopolistic or qausi-govermental structure, which, ironically enough, is because they are too free.

Potential Free Market Candidate

The freest market I can think of are economies in videogames. MMO players can acquire in-game currency by killing stuff and looting chests (similar to cryptomining), buy in-game currency with real world currency (similar to buying cryptocurrencies), and the closest thing to a government in MMO worlds are the devs..... like in smart currencies..... ;)

Anyways, inflation that MMOs suffer from is not because of government induced QE (really should be non-government, since the FED is not a governmental organization :P), but because MMO worlds have an endless supply of monsters that drop an endless supply of loots, with NPC vendors having an endless supply of in-game currency to match. All that's needed is an endless supply of time and suddenly World Of Warcraft is a post-scarcity society.

By the way, my favorite game market right now is the now defunct Global Trade System from Generation V Pokemon. Never before have I ever been able to trade a LV 5 Rattata for a shiny Celebi :)

Photo Credit: Celebi-Yoshi