No, this is Capitalism and our culture. There were and still are societies where there is very little competition between individuals or even where the concept of “competition” is unknown.
This works with small communuties living naturally, like tribes in South America. But I think with technological advancement and a cultural shift towards are more social and less individualistic society this could also work on greater scales.
Genuine question: Why? What circumstances in an “Anarchist world” would cause this behaviour?
Or the other way: If you feel like this, what in our current system stops you from acting out?