Geodesic
On properties of solutions of cooperative TU-games
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2016), pp. 73-85

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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. 
@article{IVM_2016_6_a7,
     author = {N. V. Smirnova and S. I. Tarashnina},
     title = {On properties of solutions of cooperative {TU-games}},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {73--85},
     publisher = {mathdoc},
     number = {6},
     year = {2016},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2016_6_a7/}
}
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N. V. Smirnova; S. I. Tarashnina. On properties of solutions of cooperative TU-games. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 6 (2016), pp. 73-85. http://geodesic.mathdoc.fr/item/IVM_2016_6_a7/