Volume 18, No 4, 2011, P. 77-93

UDC 519.833.5
N. V. Smirnova, S. I. Tarashnina
On a generalization of N-nucleolus in cooperative games

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).

Smirnova Nadezhda Vladimirovna ^1,2
Tarashnina Svetlana Ivanovna ^1,2
1. Saint-Petersburg State University,
35 Universitetskii ave., 198504 Saint-Petersburg, Russia
2. International Banking Institute,
60 Nevskii ave., 191011 Saint-Petersburg, Russia
e-mail: nadezhda.v.smirnova@gmail.com, tarashnina@gmail.com