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 betweensubsets of players in a manner analogous to how the Taylor series represents a function in terms of its derivativesWe axiomatize the method using the axioms that axiomatize the Shapley value—linearity,dummyandefficiency—and also an additional axiom that we call theinteraction distributionaxiom. This axiom explicitlycharacterizes how interactions are distributed for a class of games called interaction games.We contrast Shapley-Taylor values against the previously proposed Shapley Interaction Value(cf. ) thatinstead relies on a recursive construction rather than the efficiency and interaction distribution axioms.