This article is cited in 4 papers

On properties of solutions of cooperative TU-games

N. V. Smirnova^a, S. I. Tarashnina<sup>b

a</sup> 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.

UDC: 519.834

Received: 31.10.2014

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

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