RE: Can Capitalism Exist Without a State?
To look at your question up top, "can it exist?" I would have to say absolutely, and using the voluntaryist/libertarian definition.
My followup question is "is that desirable?"
For me, the questions always come up when we include "human psychology" (hereunder — in particular — greed and exploitation) in market forces.
The price of goods and services in a free market exists at the exact intersection of where the most willing seller meets the most demanding buyer. A fine example is a cryptocurrency exchange; just look at the internal market here on Steemit.
There's a tiny sliver where the actual trading happens; but there are tones of people willing to SELL at a higher price and BUY at a lower price. But they are not actually buying or selling anything, they are just "hopeful."
This is the closest we get to the economic theory of "Perfect Competition," which is a beautiful ideology of market efficiency, but tends to fall apart when we introduce human foibles, such as a question have power, or dominate, or amass wealth by sabotaging competitors.
The tendency becomes towards a tiny elite controlling most of the market, and a vast "underclass" that can't afford to participate.
But maybe I am missing something....?
That kind of stuff happens all the time in state regulated capitalism, and it is usually helped along by the state. (Corporations lobby government to pass laws and regulations that will harm their competitors or keep startups from entering the market; government passes a law that benefits a certain industry by requiring consumers to buy its product; government protects "intellectual property" on drugs and medical devices, creating monopolies in the healthcare market; etc.) So I'm not sure how getting rid of the state would increase the occurrences of this type of thing. If anything, I believe that in the absence of government, capitalism would suffer from far less abuse by the dishonest and power hungry.