There are no inherent monopolies that a typical government exercises– such as claiming the exclusive right to "legitimate force" on a large swath of land occupied by many different people. A government's typical monopoly allows it to define "legitimate"– which can include enforcing anything from speed limits, to hard labor of political dissidents in gulags.
I use the term "governance" to describe the social order under anarcho-capitalism, because "government" is defined by its monopoly. Governments don't have to earn their customers, they demand your money at the point of a gun.
Under anarcho-capitalism, law is decided by supply and demand. For example, customers would want security, so they would buy crime insurance and hire guards. Security companies would not want to go to war with rival agencies, because that is bad for profits. This gets back to the diminishing return on violence I talked about in a previous video.