Living in a world where every organism competes with every other organism we are bound to do things that would benefit us because all the others do it too and if we stopped doing it they would profit more and be better and only better genes survive.

Our world is not like that. You compete only with those that need the same resources as you do and only if the resources are not sufficient for both of you.

Another thing is, that it is seldom the case that "the more the better". For example eating more after you just ate won't make you any better.

Frankly speaking, after covering the basic needs all you can do to increase the chance of your survival is to engage in activities which will help you cover your needs in the future. And such activities don't have to be zero-sum. In other words, we can compete - then only one of the two of us can win; or we can cooperate and both win.

Anyway, I maybe got too far from your topic. I just wanted to point out that greed is not the same as selfishness. But I agree with you that selfishness is natural, because everything you do have to (directly or indirectly) increase your chance of survival - at least from the biological point of view. On the other hand, greed is more about "I wanna have more than others, I wanna win and I want you to lose", which in my opinion is rarely necessary.