Unfortunately, in cases of societal breakdown, there are very few ways in which agreement and contracts and so on can be enforced. This is why even the staunchest libertarian will admit we need governments to enforce contracts! In the absence of such a thing, personal integrity and honor play a much larger role in the scheme of things. A man's word could in fact be his life-blood.

The short of it is you have no guarantee that I will not steal cache, other than my personal beliefs and ethics prevent me from doing so.

As for me dying before your winnings can be distributed: I understand this concern. I assure you I will actively do anything in my power to prevent this. However, in apocalyptic situations this is frequently not enough :(. Of course in an apocalypse a chance at a surviving cache is still better than not having the chance, so consider it a 5th condition on the pool:

Will sophacles survive in the apocalypse to hand out the prize. If you choose yes, sign up. If you choose no, don't sign up :P.

tl; dr -- ignore that paper on my desk that says "how to fund an apocalypse stockpile without spending a dime"