Anarchy > Capitalism. Anarchy means without hierarchy. It means no man belongs to any other, to any degree without consent. It also means you economically illiterate communists and socialists can all band together in shared misery... while us capitalists will associate and contract without whomever we choose as well.
But who will keep people from killing each other?
Some kind of basic order is necessary. The right to life has to be enforced by someone.
People who don't want to get killed stop themselves from killing other people. In preventing a "bad guy" from killing a "good guy", the government also stops good guys from killing bad guys right back. You want to know how a stateless court would handle the rape of my daughter? They wouldn't. I'd have killed the fucker first.
I probably can imagine over 1000 ways of this system going totally wrong.
If you are ever going to found a state with an anarchy-like system, you better have a more solid plan than "we just kill the bad guys" up your sleeves.
Otherwise, please remind me to stay very far away from that place, there is going to be a bloodbath.
There will be ways to maintain order. Maybe neighborhoods band together to hire peace officers etc. This idea that civilization can't exist without central authority is simply wrong. Civilized people create governments, governments do not civilize people.