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Convexity and Closure in Optimal Allocations Determined by Decomposable Measures

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Abstract

A general optimal allocation problem is considered, where the decision-maker controls the distribution of acting agents, by choosing a probability measure on the space of agents. The notion of a decomposable family of probability measures is introduced, in the spirit of a decomposable family of functions. It provides a sufficient condition for the convexity of the feasible set, and the concavity of the value function. Together with additional conditions, closure properties also follow. The notion of a decomposable family of measures covers, both the case of set-valued integrals and the case of convexity in the space of probability measures.

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  1. The Weizmann Institute of Science, Rehovot, Israel

    Zvi Artstein

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  1. Zvi Artstein
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The paper is dedicate to Alex Ioffe.

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Artstein, Z. Convexity and Closure in Optimal Allocations Determined by Decomposable Measures. Vietnam J. Math. 47, 563–577 (2019). https://doi.org/10.1007/s10013-019-00344-8

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