Dividend Representations for Two Influence Assessments

Yu-Hsien Liao ()
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Yu-Hsien Liao: Department of Applied Mathematics & Green Nano Interdisciplinary Center (GNIC), National Pingtung University, Pingtung 900, Taiwan

Games, 2025, vol. 16, issue 5, 1-17

Abstract: 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.

Keywords: influence assessments; min-dividend; the stable min-value; the minimal self-stable value (search for similar items in EconPapers)
JEL-codes: C C7 C70 C71 C72 C73 (search for similar items in EconPapers)
Date: 2025
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