Mandatory Prussian education was always going to degenerate into this, if not worse. The monopoly corruption alone is sufficient to guarantee it; if we add in the explicit Prussian goals it’s overdetermined.

Further, don’t forget it’s anarcho-tyranny. The kids could form self-defence armies just like adults do. They would have both morale — bullies know they have the moral low ground — and probably organization advantage due to higher conscientiousness of the law-abiding.

Only if they did that, teachers would all of a sudden remember how to discipline. It wouldn’t be bribes this go around.

That said…

How old are these kids? Female teachers are as vulnerable to Game as any woman. It’s half the reason the bullies’ school career goes so well. However, the detail-oriented and instruction-following have a comparative advantage, once they are exposed to Game strategies. I do worry that there’s a psychological reason nine-year-olds can’t run game on purpose, but other than that…