User blog comment:Green Ninja/Dealing with Anonymous Users/@comment-1997905-20140825221151

You may request this from staff with Special:Contact/general. You will need to cite a community discussion (forum thread, blog, poll, project page, or something else) where a majority of users have voted to disable anonymous edits. However, it is also worth noting that even with such a discussion, Wikia infrequently grants this, and you may be denied anyway.

As others have mentioned, you can also contact the VSTF, however they don't babysit wikis. If your problems are coming from one person or a small group of people, the VSTF has tools for blocking all of them from your wiki, but they aren't replacement admins that will watch your recent changes for you.

Consider also that your anonymous contributors may have something to add, but are having a hard time editing. Generally, you should assume good faith, as Wikipedia does. Without a link to your wiki, I cannot be sure that this is or is not the case.