This article is cited in 2 papers

On a generalization of $N$-nucleolus in cooperative games

N. V. Smirnova^ab, S. I. Tarashina<sup>ba

a</sup> Saint-Petersburg State University, Saint-Petersburg, Russia
^b International Banking Institute, Saint-Petersburg, Russia

Abstract: We describe a new solution concept for a cooperative TU-game, called the $[0,1]$-nucleolus. It is based on the ideas of the nucleolus and the simplified modified nucleolus. The $[0,1]$-nucleolus takes into account both the constructive and the blocking powers of a coalition with all possible ratios between them. We show that this solution satisfies the following properties: nonemptiness (NE), covariance property (COV), anonimity (AN), Pareto optimality (PO), reasonableness (RE), and dummy player (DUM). Moreover, the $[0,1]$-nucleolus satisfies the individual rationality property (IR) for the class of 0-monotonic games and the single valued property (SIVA) for the class of constant-sum games. We also investigate connection between the $[0,1]$-nucleolus and some well-known solutions of cooperative TU-games such as the Shapley value, the prenucleolus, the simplified modified nucleolus and the modiclus. Tabl. 1, ill. 1, bibliogr. 8.

Keywords: TU-game, solution concept, the prenucleolus, the simplified modified nucleolus, the modified nucleolus (the modiclus).

UDC: 519.833.5

Received: 26.12.2010

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