Open market means balancing capitalism vs democracy. Property rights, fair and impartial judiciary, regulations to promote competition, and so forth.

Whereas free market means might makes right. AKA feudalism, corporatism, kleptocracy, neo-reactionary, fantasy land, etc. Basically whatever nonsense the Heritage Foundation stooges are paid to peddle.

Even though I grew up listening to the Sex Pistols, I still have no idea what anarchy is, idealized or not. I just assume its more Lord of the Flies than some hippy free love commune.

In general, idealized terms, anarchism is the belief that all transactions between people should be voluntary and non-coercive. Because states derive their power though a monopoly on involuntary coercive force, anarchists believe that no state and no interaction with a state can be morally justified.

Beyond that, anarchists seem to disagree about everything except whether or not taxes are theft or weed should be legal, and probably not even that.

Personally, I suspect anarchy simply resets the evolutionary curve of society to clan-based power structures, and that tribalism, mafias, serfdom and states proper will inevitably be reinvented.

Well, that sounds like it would work wonderfully if we had virtually infinite natural resources.

Like a lot of utopian ideals, anarchy does seem as if it wouldn't scale well.