Better to have a "me first" culture and be open about it - that way everyone knows where they stand.
Also - what's wrong with a "me first" culture? Within the boundaries of the law, surely that rewards enterprise and ability? Give me a meritocracy over some sort of perverse egalitarianism any day. Some people are ignorant, stupid, and incapable of interacting with others. They deserve to live in **** holes. Some people are unlucky and victims of circumstance. Some people are lucky and privileged. That's what happens when there are billions of people. Get over it.
Most people are reasonable and will help others rather than tread on them.