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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 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
Full-text PDF (223 kB) Citations (2)
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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.
Received: 31.10.2014
English version:
Russian Mathematics (Izvestiya VUZ. Matematika), 2016, Volume 60, Issue 6, Pages 63–74
DOI: https://doi.org/10.3103/S1066369X16060086
Bibliographic databases:
Document Type: Article
UDC: 519.834
Language: Russian
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
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\jour Russian Math. (Iz. VUZ)
\yr 2016
\vol 60
\issue 6
\pages 63--74
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