Blaming bad behaviour on 'human nature' (or even genetics) is a tiresome cop-out that has been repeated over and over again by those who keep perpetuating the ridiculous myth in question (yourself included).
Humanity lived most of its time in scarcity-like environment (due to population explosion which was AFTER the hunter-gatherer times). Our ability to find technological solutions to scarcity (abundance) is fairly new... but very little has changed on a social level.
Oh and, in case you hadn't noticed, humans who received relevant general education (I'm not talking about industrialized academic education) are not prone to competitive behavior, selfishness, or greed.
How does your 'human nature' explain notions of people volunteering their free time, ideas an energy to help others expecting nothing in return and getting nothing in return?
How do you explain the premise that when I repair people's computers and assist them in certain educational aspects (and generally help other people because I like doing it) I don't ask for compensation of any kind (in fact I refuse it outright)?
If all humans were greedy and selfish by 'nature' (followed something that couldn't be changed), then I certainly wouldn't be doing anything of the above without asking for anything in return, nor would millions around the globe volunteer for nothing.
As I said... if human behavior couldn't be changed, we'd still be living in caves.
"Human nature" is quite simple, a fallacy.