A New Interaction Index inspired by the Taylor Series

02/14/2019

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by   Ashish Agarwal, et al.

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We study interactions among players in cooperative games. We propose a new interaction index called Shapley-Taylor interaction index. 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. We axiomatize the method using the standard Shapley axioms--linearity, dummy, symmetry and efficiency--and also an additional axiom that we call the interaction distribution axiom. This new axiom explicitly characterizes how inter-actions are distributed for a class of games called interaction games. We contrast the Shapley-Taylor interaction index against the previously pro-posed Shapley Interaction index and the Banzhaf interaction index (cf. [2]).