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Izvestiya Vysshikh Uchebnykh Zavedenii. Matematika, 2016, Number 6, Pages 73–85
(Mi ivm9125)
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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.
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
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https://www.mathnet.ru/eng/ivm9125 https://www.mathnet.ru/eng/ivm/y2016/i6/p73
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Abstract page: | 222 | Full-text PDF : | 55 | References: | 58 | First page: | 19 |
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