I admit, the scenario you are describing is not something I personally prepare for, but if such a TEOTWAIKI event did occur, would it not most likely greatly reduce the human population? If so, while resources are limited, competition for those resources theoretically may not be as grave as you fear.

In any case, I would speculate the key is community. Whether you are talking a short term disaster or something longer term, I figure those that are going to thrive are those who are part of a community who can work together to get through the storm. This community building is something that is best done now, before TSHTF.