On Minimizing Influences Under Multi-Attribute Models

In classical transferable-utility models, components typically participate in an all-or-nothing manner and are evaluated under a single criterion. This study generalizes such models by allowing each component to engage through multiple acting measures and by incorporating multiple evaluating attributes simultaneously. We introduce two influence-based assessments, the stable min value and the minimal self-stable value, to evaluate fair assessments of minimal impact across multi-attribute multi-choice environments. These values are rigorously defined via axiomatic characterizations grounded in minimal influence behavior, where coalitions select activity levels that jointly minimize systemic effects. A key theoretical contribution is the identification of a unique, 0-normalized, and efficient multi-attribute potential function corresponding to the minimal self-stable value. The proposed framework enables structured and interpretable evaluation of influence in complex cooperative systems with heterogeneous participation and conflicting objectives.