Dividend Representations for Two Influence Assessments

This paper establishes dividend-based representations for two influence assessments. First, we define a system of min-dividends derived from the minimal-influence evaluation via a unique linear decomposition using unanimity-type spanning models. Building on this, we further construct a pair of internal and external min-dividends satisfying Completeness and Balancedness conditions, through which we express the stable min-value as the net difference of internal gains and external losses. We then demonstrate that the minimal self-stable value can be represented as accumulated average min-dividends across all coalitions they have participated in. Furthermore, the proposed expression also is adopted to analyze the stability of the minimal self-stable value. These results extend the classical notion of dividends into a minimal-influence-based framework with potential applications in fair resource allocation and responsibility apportionment.