The simplified modified nucleolus of a cooperative TU-game
In the present paper, we introduce a new solution concept for TU-games, the simplified modified nucleolus or the SM-nucleolus. It is based on the idea of the modified nucleolus (the modiclus) and takes into account both the constructive power and the blocking power of a coalition. The SM-nucleolus inherits this convenient property from the modified nucleolus, but it avoids its high computational complexity. We prove that the SM-nucleolus of an arbitrary n-person TU-game coincides with the prenucleolus of a certain n-person constant-sum game, which is constructed as the average of the game and its dual. Some properties of the new solution are discussed. We show that the SM-nucleolus coincides with the Shapley value for three-person games. However, this does not hold for general n-person cooperative TU-games. To confirm this fact, a counter example is presented in the paper. On top of this, we give several examples that illustrate similarities and differences between the SM-nucleolus and well-known solution concepts for TU-games. Finally, the SM-nucleolus is applied to the weighted voting games.