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Published in:
2009 | OriginalPaper | Chapter
A Lyapunov-Type Theorem for Nonadditive Vector Measures
Author : Nobusumi Sagara
Published in: Modeling Decisions for Artificial Intelligence
Publisher: Springer Berlin Heidelberg
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We prove the convexity and compactness of the closure of the lower partition range of an ℝ
n
-valued, nonatomic, supermodular capacity, employing a useful relationship between convex games and their Choquet integrals. The main result is applied to fair division problems, and the existence of Pareto optimal
α
-fair partitions is demonstrated for the case of nonadditive measures.