Before revision:  It decomposes the value of the game into terms that model the interactions between subsets of players, analogous to how the Taylor series represents a function in terms of its derivatives of various orders .
After revision:  It decomposes the value of the game into terms that model the interactions between subsets of players, analogous to how the truncated Taylor Series decomposes the function value at a certain point using its derivatives at a different point. In fact, we show that the Shapley Taylor index is equal to the Taylor Series of the multilinear extension of the set-theoretic behavior of the model .