Split player might cause inconsistent shapely value

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I was trying to compute the shapely value for a machine learning model. And run into an issue that might conflict with the uniqueness of shapely value.

Suppose when $N$ player in the game, and there is a fair way to divide contribution to them. Now if I pick a random player and split his gaming strategy into two surrogate players and compute the $N+1$ player's shapely value.

And aggregate the shapely value over two surrogate players into the original player and run into an issue such that they don't match to the $N$ player's values.

I'm wondering what's the loophole in my operation? And how can I address the problem?