The nucleolus is well-posed

Vito Fragnelli; Fioravante Patrone; Anna Torre

doi:10.1016/j.jmaa.2005.03.090

The nucleolus is well-posed

Vito Fragnelli
, Fioravante Patrone
, Anna Torre

Research output: Contribution to journal › Article › peer-review

Abstract

The lexicographic order is not representable by a real-valued function, contrary to many other orders or preorders. So, standard tools and results for well-posed minimum problems cannot be used. We prove that under suitable hypotheses it is however possible to guarantee the well-posedness of a lexicographic minimum over a compact or convex set. This result allows us to prove that some game theoretical solution concepts, based on lexicographic order are well-posed: in particular, this is true for the nucleolus.

Original language	English
Pages (from-to)	412-422
Number of pages	11
Journal	Journal of Mathematical Analysis and Applications
Volume	314
Issue number	2
DOIs	https://doi.org/10.1016/j.jmaa.2005.03.090
Publication status	Published - 15 Feb 2006
Externally published	Yes

Keywords

Cooperative game
Lexicographic order
Nucleolus
Tikhonov well-posedness

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10.1016/j.jmaa.2005.03.090

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abstract = "The lexicographic order is not representable by a real-valued function, contrary to many other orders or preorders. So, standard tools and results for well-posed minimum problems cannot be used. We prove that under suitable hypotheses it is however possible to guarantee the well-posedness of a lexicographic minimum over a compact or convex set. This result allows us to prove that some game theoretical solution concepts, based on lexicographic order are well-posed: in particular, this is true for the nucleolus.",

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AB - The lexicographic order is not representable by a real-valued function, contrary to many other orders or preorders. So, standard tools and results for well-posed minimum problems cannot be used. We prove that under suitable hypotheses it is however possible to guarantee the well-posedness of a lexicographic minimum over a compact or convex set. This result allows us to prove that some game theoretical solution concepts, based on lexicographic order are well-posed: in particular, this is true for the nucleolus.

KW - Cooperative game

KW - Lexicographic order

KW - Nucleolus

KW - Tikhonov well-posedness

UR - https://www.scopus.com/pages/publications/29144507474

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DO - 10.1016/j.jmaa.2005.03.090

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JO - Journal of Mathematical Analysis and Applications

JF - Journal of Mathematical Analysis and Applications

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ER -

The nucleolus is well-posed

Abstract

Keywords

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