I designed & wrote a review system and recommendation system for an online recipe-sharing website a long time ago. The recommendation system didn't require any game theory, just stats and sets, but thinking about the problems I had to solve with the reviews, they were definitely game-theory-y (though I didn't think about it that way at the time).
The problem that the site I worked on faced was that people could be both authors and reviewers, so there was a certain pressure to "pump up" their own recipes' stats perhaps by "pushing down" others. So there was a balance that had to grow organically from our rules to offset that selfish impulse; we did this with a per-user reputation score based on other peoples' reviews of their recipes and how helpful other people thought their reviews were. In retrospect I wish I had more rigorously applied some game theory here.