Worldhistory.org/empire/ says “At its core, an empire is the domination of one state by another. This idea lies at the heart of the common use of the term ‘empire’ and is as old as state-building itself.”
Darwin said, “More individuals of every species are born than can possibly survive.” Overpopulation forces the “frequent struggle(s) for existence” that drive “natural selection” of living characteristics including our ability to feel passions such as fear of others.
Through history, as human overpopulation presses “us” into competition with “others,” does “empire” simply describe a common result? One “us” group eventually succeeds in dominating, sometimes by decimating, sometimes enslaving “others” who may now be required to “share” resources and abilities?
First of all, your view only works in a Malthusian reference. However the increasing number of humans and the developpment of farming and technology to accomodate for that many humans kinda disproves the idea that there is an overpopulation of humans in Darwin’s sense. The lack of ressources has more often than not been caused by humans rather than scarcity. Empire therefor cannot really be an overpopulation-handling strategy. Otherwise overpopulation of what group ? Central or peripheral ? Which peripheral group specifically ? What about all the states and human settlements that have always existed outside of empire throughout History ?
Now about empires themselves, the definition is somewhat lacking. I’d rather turn to Burbank and Cooper for their study of Empires throughout history. They define an empire as the handling of diversity with a large state comprised of a central group and peripheries. Those peripheries being more or less integrated within the empire. Worldhistory.org’s definition isn’t really operational especially because it shows a bilateral relation and uses the same concept « state » on both sides of the relation. Furthermore, you seem to understand the word domination as something necessarely in an attempt to erase another group. Which isn’t the case as Burbank and Cooper demonstrate. Contrary to Nation-states, Empires maintain the diversity and the various peripheral groups, often giving them autonomy to certain extent. Slavery and genocide aren’t inherent to empires, and most examples of extermination either target one specific group within an empire for specific punctual reasons while the other groups either help or remain unharmed. The recent examples of genocide are linked specifically to the idea of Nation-states that go against the nature of Empires as their purpose is to get rid of diversity and historically has done so through extreme violence, even genocide.
So to answer your question, first of all the question only makes sense if you agree with Malthus that has time and time again been proven wrong or at least not right. Then the definition of empire you use isn’t useful as it isn’t clear and makes it possible for you to completely leap to conclusions that historically don’t match what empires have done. Finally, the most useful historical definition of empires actually goes against your point as it maintains diversity instead of erasing it like Nation-states have done in recent history.