The keyword is totally unique in the eyes of the search engines, and there are strong rules in these contests.

Some of the general important rules of seocontests.
1. No black hat search engine optimization allowed
2. No one from the official announcement website can enter this contest.
3. No Spamming of keywords and website
4. No cloaking or keyword stuffing

These contests generally are started with a time frame given to show the results in search engine results pages.

These are some of the general tips to rank better for the contest.
1. Try to get a older domain name rather than a new one, this is because there is a myth that search engines rank old domains better.
2. Never try to add the contest keyword more than 10 times to your contest webpage because this will result in keyword stuffing.
3. Add meta tags to your contest page which may include title, keywords, description and robots tag.
4. Add H1 , H2, and H3 tags correctly with the keyword in the first H1 tag.
5. Try to add unique contest to your webpage, which is totally fresh, as search engines like fresh content.
6. After the onpage seo is completed , start doing link building by exchanging links with relevant websites.
7. Add a sitemap to your website and continue with the link building.

If these steps are done perfectly , you can make sure that your webpage tops the search engine result pages.