Anarcho-Capitalism is the belief that it is practical to replace government coercion with voluntary private agreements.
This idea has several failure modes. The most obvious is portrayed in Kurosawa's great Seven Samurai. If you haven't seen it, I beg you to do so a soon as possible. It is a great piece of cinema.
If you have, you will recall that during the 16th century, a time of civil war, a Japanese village discovers that they are on the do list of about 40 marauding bandits, who decide to postpone looting until the harvest is in. After consultation with the local matriarch and crone, the villagers agree that their best course of action is to hire a small group of samurai for protection. Hungry samurai, since the village can only afford to pay room and board.
Fortunately, the villagers delegated to hire security encounter Kambei Shimada, an aging, altruistic samurai played by the great Takashi Shimura. He concludes that the village defense requires no less than seven samurai, more than the delegates were authorized to hire, and eventually assembles a team, many of whom follow him for reasons beyond the meagre room and board offered by the village.
After Kambei arrives at the village, he begins planning a defensive perimeter that will leave several farms undefended because they are indefensible. The outlying farmers attempt to opt out of the defense agreement and defect. They are quickly coerced back into the ranks by the samurai. Because the protection agency that the village voluntarily hired can coerce, and it will coerce if that's the only way to win, and it was. And these are the good guys.
Italian history is full of condotieri who concluded 'Nice city-state you've got there. I'll take it.'