Nonlinear Attribution Improves Player Ranking in Cooperative Games.

The Shapley value is a cornerstone in attribution problems, known for satisfying key axioms like linearity and efficiency. However, this research highlights a critical flaw: its linearity can make it unreliable for ranking player contributions, particularly when evaluated using the inclusion AUC metric. The issue stems from the Shapley value acting as a linear operator with a large null space, meaning it can't distinguish between certain non-negligible perturbations in player contributions. To overcome this, the paper proposes a new class of nonlinear axiomatic attribution methods. Drawing inspiration from the least core, a known nonlinear alternative to the Shapley value, these methods are designed to retain essential axioms while introducing nonlinearity. Each method yields a unique contribution vector by solving a minimization problem that aims to approximate utility functions more faithfully. Experimental results demonstrate that these nonlinear methods can be more effective than Shapley value variants (even those relaxing the efficiency axiom) in terms of the inclusion AUC metric. This suggests they provide a more accurate and reliable way to identify and rank the positive contributions of players in cooperative game theory settings, which has implications for various real-world attribution scenarios.