Convexity and Closure in Optimal Allocations Determined by Decomposable Measures

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 func...

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Bibliographic Details
Published in:Vietnam journal of mathematics 2019-09, Vol.47 (3), p.563-577
Main Author: Artstein, Zvi
Format: Article
Language:English
Subjects:
Allocations
Concavity
Convexity
Decision making
Decomposition
Mathematics
Mathematics and Statistics
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Summary: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.
ISSN:2305-221X
2305-2228
DOI:10.1007/s10013-019-00344-8