Deep learning is expected to revolutionize many sciences and particularly healthcare and medicine. However, deep neural networks are generally “black box,” which limits their applicability to mission-critical applications in health. Explaining such models would improve transparency and trust in AI-powered decision making and is necessary for understanding other practical needs such as robustness and fairness. A popular means of enhancing model transparency is to quantify how individual inputs contribute to model outputs (called attributions) and the magnitude of interactions between groups of inputs. A growing number of these methods import concepts and results from game theory to produce attributions and interactions. This work presents a unifying framework for game-theory-inspired attribution and k^{\text{th}}-order interaction methods. We show that, given modest assumptions, a \underline{unique} full account of interactions between features, called synergies, is possible in the continuous input setting. We identify how various methods are characterized by their policy of distributing synergies. We establish that gradient-based methods are characterized by their actions on monomials, a type of synergy function, and introduce unique gradient-based methods. We show that the combination of various criteria uniquely defines the attribution/interaction methods. Thus, the community needs to identify goals and contexts when developing and employing attribution and interaction methods. Finally, experiments with Physicochemical Properties of Protein Tertiary Structure data indicate that the proposed method has favorable performance against the state-of-the-art approach.