Hello just reading your reply. Maybe you would call me a crapitalist but I don't think that skinning my neigbours makes perfect sense not literally and nor figuratively.
It goes directly against my principles. But then again maybe you would give me another name.

I do no think I understand the question but I will try to answer. A third party like a government could exist in market socialism. In yugoslavia they had market socialism (before being bombed by America). It worked well and the government did not step in with strict regulations.  

Capitalism is free trade with private property.

reply to your reply to free:
Non aggression principle is a common one for "anarchist capitalists" as they will tell you. However, people will hire armies to protect what they see as "theirs". For example we could even go as far as saying North Korea is justified because it is private property, and anarchist capitalist in its ideals because it can trade freely with other countries.

No, the functions of gov't are done by the folks that need that work done, or not at all.
Vigilante neighbors tend to pacify neighborhoods, so need for cops.
Everything is free, so no need for social workers.
Accounting is done for reorders and by robots, so no accountants or cashiers.
The honor system and reputation will keep most people in line, and criminals will suffer at the hands of their victim's friends.
Yes, I know, that can get out of hand, but is what we have now where the killing is done with impunity by cops better?
You can do as you please, if you want to trade your widget for somebody's gadget and that is agreeable to both, then feel free.
But, if you feel like starving kids in Africa and bombing kids in Syria because your bottom line needs enhancing from last  year, that is an issue to be addressed by the locals in the local customary manner.
Towns of like minded individuals will spring up and you will not want to associate with some of those, and they will be free from your disdain.
Prostitution is illegal, it won't be.
Drug dens are illegal, they won't be.
Gambling halls are illegal, they won't be.
But none of those will be in a neighborhood that won't tolerate them.
If that is not your scene instead of sending thugs to kill some people we will allow them to live over there in peace.
We will freely disassociate ourselves from them, and they with us.
Most of the problems of the world can be solved by simply ending the elephant in the room, rule by force.