Constructive and blocking powers in some applications

Svetlana Tarashnina^a, Nadezhda Smirnova<sup>b

a</sup> St. Petersburg State University, 7/9 Universitetskaya nab., St. Petersburg, 199034, Russia
^b Higher School of Economics, Department of Applied Mathematics and Business Informatics, Soyuza Pechatnikov ul. 16, St. Petersburg, 190008, Russia

Abstract: We investigate the prenucleolus, the anti-prenucleolus and the $SM$-nucleolus in glove market games and weighted majority games. This kind of games looks desirable for considering solution concepts taking into account the blocking power of a coalition $S$ with different weights. Analytical formulae for calculating the solutions are presented for glove market game. Influence of the blocking power on players' payoffs is discussed and the examples which demonstrate similarities and differences comparing with other solution concepts are given.

Keywords: cooperative $\mathrm{TU}$-game, solution concept, prenucleolus, $SM$-nucleolus, constructive and blocking power, glove market game, weighted majority game.

Language: English

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