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EnglishThe 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.
The nucleolus is well posed / PATRONE F.; FRAGNELLI V.; TORRE A.. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - :314(2006), pp. 412-422.
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| Titolo: | The nucleolus is well posed | |
| Autori: | ||
| Data di pubblicazione: | 2006 | |
| Rivista: | ||
| Citazione: | The nucleolus is well posed / PATRONE F.; FRAGNELLI V.; TORRE A.. - In: JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS. - ISSN 0022-247X. - STAMPA. - :314(2006), pp. 412-422. | |
| 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. | |
| Handle: | http://hdl.handle.net/11571/134474 | |
| Appare nelle tipologie: | 1.1 Articolo in rivista |
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