User blog comment:B214/Question and Answers/@comment-50.11.177.49-20130615040443/@comment-33447191-20130617054152

The Four Great Satans don't participate in the Rating Game, their servants can, however, none have shown any interest in doing so. Also, like I mentioned earlier, Vali's final goal is Great Red to prove that White stands above Red. If he were to succeed, there's no telling what would happen, as Great Red is the one responsible for keeping the World in balance. Also, it may not be so easy, as in the eyes of the High-Class Devils, they will still be seen as a threat. Kuroka killed her master and escaped, even if she was doing it to protect her sister, they wouldn't see it that way.

Anyways for the time being, it would be a whole lot easier if they just live their separate lives to avoid conflict.