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.

The counterpoint to immortality is generation ships -- and as witnessed by today's society, humanity can't sustain peaceful coexistence across even a few generations. I would bet that by the time such a spaceship encounters new life, the most domineering and conquest-happy in humanity will have outwrestled curiosity and desirelessness.