Analytical anarchism is a subset of political economy that takes neither rules as given nor assumes that monopoly enforcement of such rules exists. This approach is the positive study of endogenous rule formation by individuals within a particular society. Such rules emerge out of the self-interest of such individuals, though not necessarily from any deliberate design. We outline and explain two theoretical approaches that have been used to illustrate various historical cases of anarchism across time and place. We distinguish between an exclusionary approach to analytical anarchism and an inclusionary approach to analytical anarchism. Though these two approaches are not mutually exclusive, they are distinct from each other, in that they illustrate alternative mechanisms under which the conditions of anarchy can be relatively peaceful and productive.