I am trying to find a property which can help to analyse the composition of a cost/profit division and which allocation rules (e.g., Shapley value or nucleolus) would satisfy it.
In short, the idea is that if I divide a player into more players (subplayer), they should still get the same as the original player (the sum of the profit/cost of the subplayers is equal to the one of the original player).
The characteristic function and the profit/cost for all the other players should remain the same as well.
I am sure that someone has studied this before. So far I looked at different versions of monotonicity but they do not seem to reflect what I am looking for.
The simple option would be to divide the problem in two different games (e.g., based on the profit/cost of the player make a game for the sub players to see how to divide it), but I think that if you plug the subplayers instead of the original player they should still get the same as the original player.
Thanks in advance!