Here populations with a society structure are modeled by so-called resource-dependent branching processes (RDBPs).
A RDBP is a discrete time branching process (BP) in which individuals are supposed to have to work to be able to live and to reproduce.
The population decides on a current society form by a policy, that is a prescription of rules how available resources are to be distributed among the individuals.
Apart from a classical result on so-called complete convergence, it is mainly based on theorems for stopping times on sums of independent and identically distributed order statistics (ref.
Extreme Capitalism cannot be stable because, unless resources are abundant, it would either die out or be quickly outnumbered by competing societies streaming into the vacuum.
However both form in the long run (in terms of the effective of populations) an envelope of any society whatever sophisticated its policy may be.