That's what we tried and it ended up all users liking a lot each other during the first half of the competition period, which was useless and stuffing likes counters.
We put the forum in the read-only mode for a few minutes when we started, and copied likes counters.
We're going to do the same when the competition ends.
Shouldn't be a problem if you set start/stop time when everyone is sleeping
We tried to let users compete on reaching a particular level. This was useful in that it combines a lot of things people have to do to get there, which is beneficial for your forum and can be called "activity" altogether. However, we ended up it was very difficult to explain to the end users what exactly they should do and how they can see their progress and how everything is counted, so we just gave up on this idea.
We're now thinking about:
- most invitations who reached a particular level
- most viewed topic based on google analytics (will let users post links here and there and share with friends)
- most liked image (media is much better than text even if it's spammy but still attractive).