As a law student with a very strong interest in copyright law, I'd like to make a couple of points based on English law. English law is the basis for most common law jurisdictions, so a lot of this will apply if you're in the US, Canada, New Zealand, etc.
First and foremost, you cannot copyright an idea. You can copyright the implementation
of that idea but the buck stops there. If it didn't, I'd be getting my arse handed to me by Paramount pictures for my space opera stories and also by the BBC for the time I ran a strip about a time-travelling meddler in other peoples' business.
Secondly, in order to get anything more than a restraining order for alleged copyright infringement, you have to be able to show that you lost out somehow thanks to the infringer's actions. In webcomic terms this is likely to be a demonstration that the infringer made money specifically from the material that infringes your copyright. That's not going to happen in terms of webcomics, because most don't make money.
It's true that there's a writer out there who can't get one of their books published because a fanfiction writer made a big to-do about how the book infringed on ideas they introduced in a fan fiction but that's at the extreme fringe of the law and to be honest, unless the fanfiction writer really has a cut-and-dry case (in which case, boo hiss to the author for stealing a fan's ideas!) then the publisher is urging too far toward caution.
Just because you run a competition doesn't mean you should be too scared of 'stealing' ideas. Ideas are ten a penny and aren't copyrighted anyway. If you're that scared of fall-out, either don't run the competition or get independent volunteer judges to vet the entries for you.