Rethinking Least-Core Computation in Contextual-Distractor Games

Game-theoretic attribution explains a model by assigning credit to its features or training examples. The least core has attracted interest as an alternative to Shapley-style averaging because it can expose players that cause substantial harm in rare, high-value contexts. However, least-core allocations are generally nonunique, and the choice of allocation can affect the resulting explanation. In this study, we investigate how payoff selection and coalition sampling affect least-core attribution. Our experiments show that selector choice matters for distinguishing useful and harmful contributions, and that sampling can degrade harmful-player identification across the tested selectors even when useful players remain well identified. These observations motivate efficient computation with all coalition constraints and a well-defined selector. We introduce entropic least core (ELC), a smooth approximation whose unique minimizer follows a continuous path along the temperature to the nucleolus, a classical refinement of the least core. Our experiments show that ELC approximates the nucleolus faster than an LP-based nucleolus solver while retaining small payoff errors, with further GPU acceleration at larger problem sizes. ELC is particularly superior in retrieving and ranking harmful players in the contextual distractors setting.