Basically the An-cap argument is that logically there is no need, role, or reason for the state to exist within capitalism. In theory and practice this means not just open competition between capitalists in the market but also open competition between capital and labor, plus open competition between labor and labor.
The state is a feature of all class societies and is effectively the machinery of government - or if you prefer the executive - for the ruling class. The emergence of the nation state corresponds with the social development of capitalism where it was found necessary to regulate production, competition and trade so that the growth of monopolies were restrained through anti-trust laws and other legislation. In practice this means whoever controls the state has the political power to regulate the balance of rivalry between the different sectional interests of the capitalist class.
This is the current status quo and there’s no signs of it changing whilst capitalism lasts. For its through their common experience both the nation state and a majority of the capitalist class have reached an agreement that such a settlement is in their collective interests for legitimizing the private ownership of property by the provision of a coercive machine (police, judiciary, armed forces, schools, etc.) for conserving the monopoly by the capitalist class of the wealth taken from the workers in a geographical area.
And its specifically on this point that the theory of the an-caps fails. For without the institution of the nation state there’s no legitimacy on all transactions worthy of consideration.
