Abstract
We prove the convexity and compactness of the closure of the lower partition range of an ℝn-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.
This research is supported by a Grant-in-Aid for Scientific Research (No. 18610003) from the Ministry of Education, Culture, Sports, Science and Technology, Japan.
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Sagara, N. (2009). A Lyapunov-Type Theorem for Nonadditive Vector Measures. In: Torra, V., Narukawa, Y., Inuiguchi, M. (eds) Modeling Decisions for Artificial Intelligence. MDAI 2009. Lecture Notes in Computer Science(), vol 5861. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-04820-3_7
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DOI: https://doi.org/10.1007/978-3-642-04820-3_7
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