If your point is to prove that the patterns of domination and conquests that exist here will necessarily exist in the stars too, then I'm afraid your thought experiment is deeply flawed.
If ever we are able to journey through the interstellar medium, we ought to have achieved immortality by then. We'll probably live as deincarnated beings in virtual worlds, free from any desire to grow exponentially, having realized this is deeply unsustainable and pointless once you have mastery over physical reality.
Read Diaspora by Greg Egan, perhaps it can cure you from this simplistic vision of the far future we have inherited from the 50s pop SciFi books.