Integrating axiomatic and dynamic mechanisms under industrial management situations: game-theoretical analysis

In numerous industrial management situations, multiple departments or units engage in complex, multi-grade interactions that influence overall organizational decisions. This study introduces a new assessing scheme that accounts for units' activity grades within such a situation. Unlike the Shapley value and the equal allocation of nonseparable costs, this assessing scheme remains computationally linear due to its single-pass step-grade decomposition, and it preserves several useful properties under any graded coalition. By applying specific reduction and excess function, several axiomatic and dynamic results are established to characterize the scheme's consistency and stability. These theoretical findings, generated from game-theoretical analysis, offer actionable insights into key participating units, including stakeholder engagement, incentive structures, and coalition formation, thereby enhancing the strategic decision-making processes in real-world industrial management contexts.