Anarcho-capitalism, or can we do away with the state

The author outlines a basic framework for anarcho-capitalism, a stateless social order in which safety, law and adjudication of disputes are provided by private companies (private defense agencies) competing with each other in the free market. In the course of presentation, three fundamental problems of anarcho-capitalism are addressed. (1) Is a peaceful cooperation among agencies possible? (2) Would agencies respect the rights of their customers? (3) How would the law look like in an anarcho-capitalist society? The last problem is especially vexing,since anarcho-capitalists seem to be caught up in a contradiction here. On one hand they are proponents of a specific moral theory (based on non-aggression principle), on the other hand they do not allow for any central, monopolistic agency to impose that moral theory on society. Is it possible for the law in the anarcho-capitalist society to be simultaneously produced by competing agents and remain libertarian at the same time?