I’ve got news for you, then. This is literally the world we live in right now.
And the only reason we have a functioning civilization is because there is indeed a state monopoly on violence. If the government collapsed tomorrow (due to nuclear war, pandemic with a high mortality rate, supervolcano eruption, asteroid impact, etc.) civilization would promptly collapse as well as the survivors banded together in small groups and started warring with their neighbors.
And yes, people would be killing others and taking their resources if they felt they could get away with it. This has been human nature since before there were humans. In such a situation, the only reason we do cooperate is because we have made a calculation that it might benefit us.