Rulers can only intervene under special circumstances IIRC. We don't know if there are among the LPB or PB though it's likely. This is a war anyway and the game has been allowed by the Admin.
The war was set up by Traumerei and have an admin permission.
And Gustang doesn't, he created a lie to legitimize the war. I don't see any permission for the Po Bidau family.
The game with the prize is Baam was set up by Khun A.A. The game with the prize is Enkidu was set up by Bellerire. I don't see any admin here. The game was possible because Gustang and Traumerei agreed to participate.
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The rulers of the floor depend on whose floor it is. Except for the 1st and 40th floors, all 132 floors are managed by different organizations.
For example, the ruler of the 44th floor is Khun Royale Elliot, so this floor is managed by the Khun family, as are other families.
In addition, the ruler may be a family heads or there may be no ruler (the Zahard Empire will manage the floors).
So branch head can be a ruler, but a ruler of the floor that is managed by the Lo Po Bia family.
This is a good question. I would have assumed at least traumerei and gustang were rulers of the floors where their motherships reside but nowadays it seems pretty feasible they don't bother with these type of things beyond maybe selecting someone to rule their floors. It's not necessarily the case that the family's top brass are also the rulers of their floors.