Tags indicate what a question is about. If a question is tagged competition, that means it's about competitions. Not that it's about a specific competition. A question about the SHA-3 competition should not be tagged competition, unless it's about running competitions in general and just happens to use SHA-3 as an example.
I don't think we should have a competition tag. Crypto algorithm design competitions are not so frequent that we have questions about how they're run, and running competitions is mostly off-topic here anyway. A question about competitions would have to be specific to crypto competitions to make sense on this site. I think if the tag existed, it would be mostly used by people who are taking part in a capture-the-flag competition.
From the tag FAQ on the main meta:
Tags are for sorting your question into specific, well-defined categories. Each tag should by itself refer to a specific category. If a tag only makes sense when used in combination with another tag (like '2005' with 'sql-server', 'visual' with 'studio', or '3.5' with '.net'), it's a meta tag.