When debating an ancap there are two common arguments you will hear. One is that "the market will provide it" and the other is that "we will defund the company we are dissatisfied with and fund a different one that provides better service." When making these arguments, they will not theorize how the market will provide the good or service, and they will not explicate how they can switch providers if there is currently only one that exists. This does not mean that ancaps have not theorized about certain issues but when discussing these potential problems with neo-ancaps theory is usually unimportant to them. This unfortunate characteristic more often than not leads to dogmatic assertions and a priori conceptualization.
In the debate, I mentioned two things that are noncontroversial economic theories. One is about natural monopolies and the other is about airlines (my ancap opponent brought up airlines). The point I made about natural monopolies is that often times it is more efficient to have one utility company to provide a service over a geographic region. This is because of the extremely high start up costs and they do not reach diseconomies of scale, i.e., it is cheaper for them to provide the natural good to more people than less people. Thus, the people of this region can get their water at a cheaper price. To stop this single company from charging obscene prices I posited a solution that a governing agency could hinder them from doing so. (NOTE: I said governing agency, not government. Could the free market handle this? possibly, however, complications arise. I think this could be one justified role of a LOCAL government.)
In response to my argument the ancap asserted that there has never been a natural monopoly, claimed I don't know anything about how the market works, and called me a socialist. It seems as though the original Anarcho-Capitalistic Dogmatism is vindicated once again.
Now I would like to transition to the point of how airlines have barriers to entry. The ancap brought up airlines in an attempt to refute my brother's point about the perfect competition model. This was surprising to me because I believe it actually refutes the ancap argument that people can simply "switch providers".
There are major barriers to entry for airlines. High costs, few firms, and airlines can control their prices (minus of course some costs like the changing prices of fuel). These barriers to entry make it extremely difficult for a new firm to enter the market and survive. This is because one must have a lot of capital to start up a new airline. With such high costs there is more risk, which in general can discourage investors. Moreover, with such few firms and their control over the prices it is easy for existing firms to lower prices to cause new start up firms to fail. (I would like to point out that when I argued this he acted as if it was ridiculous but asserting something to be ridiculous is not the same as proving it. The argument I was presenting is studied in depth by economists, it is known as the field of Industrial Organization, hence it is the theory of how certain industries are organized) The problem with the airlines could also be an issue when it comes to a police force or national defense. The ancaps frequently argue that the market will provide a police force and a national defense but the fact of the matter is that it is hard to switch services when it is a service outside of perfect competition. This is ultimately why I think ancaps need perfect competition in order for their theory that consumers can switch providers to be plausible.
I would also like to point out that I am not arguing that these potential problems are examples of market failures where the government is needed to intervene. I am simply pointing out that these situations are much more complex than the ancap would like you to believe. The assertion that the market will fix it or we will switch providers is much too simplistic for these complicated issues.