I have never heard of a contest for GDDs. A money prize is unlikely in the extreme. I think you should ask a different question. What is it you really need, what can we tell you that'll help you get where you're trying to go?

I haven't really heard of anything like that either, but perhaps GameSprout (recent GDNet topic) is what you're looking for?

Weird but interesting question, it kinda makes me curious as well. Would've been a cool thing for some people I guess. The only problem with a competition, as I see it, is the difference between this and just pitching your idea to a publisher the standard way. Either it's the big guy (i.e. publisher) who decides the winner, in which case its just like pitching your idea normally (and thus redundant). Or, it's decided by vote, in which case the publisher must potentially forego his own Brand and preference to cater to a public opinion determined by random people. Not only do they need to have actually heard of this competition, but decided to participate as well (which in sum may not be an adequately large or accurate focus group, unless the competition is thoroughly adverticed).

Both are unlikely, IMO. Some publishers might perhaps try this, though. It could be interesting to make games based on public opinion, as long as that opinion comes from relatively educated people. For anything factual, meritocracy is usually better than democracy. But I imagine that one could advertice this competition on Gamasutra, Gamedev and various zines (IGN, PC Gamer, GameSpot, and so of) as a major event. It could be an annual or similar event. That would at least attract the attention of a good number of fellow game developers, hardcore gamers and design enthusiasts (which might be good and relevant enough for a publisher to consider it).

competitions for grants

Oh, grants. That's an entirely different kind of thing. You need to research grants, not GDD contests.

1. Maybe I could submit my GDD to a studio.

2. Would any of you know where to start on that? I know what publishers might take a look, but I'm not sure how to begin and get their attention.

1. Maybe you could, but studios (developers) don't have money. Publishers do.

2. Read FAQs 11, 21, and 35 at http://sloperama.com/advice.html

my Intro to Game Design instructor at my college strongly urged us to get our GDDs out there

Just curious, what city and state are you in?

I'm going to move this to the Business and Law forum since it's more about getting funding or grants than design.

Maybe I could submit my GDD to a studio. Would any of you know where to start on that? I know what publishers might take a look, but I'm not sure how to begin and get their attention.

In addition to the link Tom provided above (and his other helpful lessons!) I also recommend reading through "preparing a product pitch" ,"preparing a game demo", and "funding for game projects", as well as Dan Marchant's other helpful articles; there are some industry overview articles towards the bottom of the list which will probably provide some good incite into the industry.

You might also consider crowd-funding (perhaps through Kickstarter or Indiegogo).

I don't actually know much about the specifics of applying for grants, but many areas do offer them under various terms and conditions, so it's probably worth doing further research.

I've just noticed another user appears to be in a similar position -- some of the responses to his question may also be helpful to you!