OOC? "out of control" maybe? My weakness is non-standard acronyms.

I thought Shinku explained the Alice Game to Jun in the first season.

All of the dolls fight each other, as it was the only way that Enju/whatever his other names are, could find to create 'the perfect girl.' That's why it was sad when you found out Suigintou was broken and uncompleted, and Shinku had said Suigintou's feelings for their father were the most pure. Suigintou had wanted to prove to their father that despite her broken/unfinished status, that she was capable of being prefect too.

As the dolls fight each other, they steal the others' Roza Mystica. When one of the dolls has all of them, and the rest are turned into junk, and Alice, the perfect girl, is born. That's the winged girl breaking out of the egg they show in the opening of the first season and at various other places in this one.

That's the end of it, as their father would have created the perfect daughter. The Alice Game is the one any only, end all purpose to their existence, at least according to the the others not allied with Shinku.