The Nucleolus in Multiobjective n-person Cooperative Games

In this paper, multiobjective n -person cooperative games are defined, and the nucleolus is considered in such games. First, a multiobjective game is reduced to single-objective games by using the scalarizing methods of multiobjective programming, i.e., the weighting coefficients method and the weighted minimax method. Second, the nucleolus is defined directly in a multiobjective n-person cooperative game. Computational methods for deriving the nucleolus are shown when excess functions are defined as distance from the ideal point or a Pareto optimal point.