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Izv. Vyssh. Uchebn. Zaved. Mat., 2016, Number 6, Pages 73–85 (Mi ivm9125)  

This article is cited in 2 scientific papers (total in 2 papers)

On properties of solutions of cooperative TU-games

N. V. Smirnovaa, S. I. Tarashninab

a National Research University "Higher School of Economics", 3 Kantemirovskaya str., Saint-Petersburg, 194100 Russia
b Saint-Petersburg State University, 35 Universitetskii Ave., Saint-Petersburg, Petergof, 198504 Russia

Abstract: In the capacity of a solution concept of cooperative TU-game we propose the $\alpha$-$N$-prenucleoli set, $\alpha\in R$, which is a generalization of the $[0,1]$-prenucleolus. We show that in a cooperative game the $\alpha$-$N$-prenucleoli set takes into account the constructive power with weight $\alpha$ and the blocking power with weight $(1-\alpha)$ for all possible values of the parameter $\alpha$. Having introduced two independent parameters we obtain the same result – the set of vectors which coincides with the set of $\alpha$-prenucleoli. Moreover, the $\alpha$-$N$-prenucleoli set satisfies duality and independence of an excess arrangement. Finally, the covariance property has been expanded. Some examples are given to illustrate the results.

Keywords: TU-game, $N$-prenucleolus, $SM$-nucleolus, $[0,1]$-prenucleolus, $\alpha$-prenucleoli set, duality.

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English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, 60:6, 63–74

Bibliographic databases:

UDC: 519.834
Received: 31.10.2014

Citation: N. V. Smirnova, S. I. Tarashnina, “On properties of solutions of cooperative TU-games”, Izv. Vyssh. Uchebn. Zaved. Mat., 2016, no. 6, 73–85; Russian Math. (Iz. VUZ), 60:6 (2016), 63–74

Citation in format AMSBIB
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\by N.~V.~Smirnova, S.~I.~Tarashnina
\paper On properties of solutions of cooperative TU-games
\jour Izv. Vyssh. Uchebn. Zaved. Mat.
\yr 2016
\issue 6
\pages 73--85
\mathnet{http://mi.mathnet.ru/ivm9125}
\transl
\jour Russian Math. (Iz. VUZ)
\yr 2016
\vol 60
\issue 6
\pages 63--74
\crossref{https://doi.org/10.3103/S1066369X16060086}
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\scopus{https://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-84971255077}


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    Citing articles on Google Scholar: Russian citations, English citations
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    This publication is cited in the following articles:
    1. Svetlana Tarashnina, Nadezhda Smirnova, “Constructive and blocking powers in some applications”, Contributions to Game Theory and Management, 10 (2017), 339–349  mathnet  mathscinet
    2. Maria Elnova, Nadezhda Smirnova, “Constructive and blocking power in marine logistics”, Contributions to Game Theory and Management, 11 (2018), 42–52  mathnet
  • Известия высших учебных заведений. Математика Russian Mathematics (Izvestiya VUZ. Matematika)
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