N-Person Cooperative Games with Multiple Scenarios

In this paper, solution concepts for an n-person cooperative game with multiple scenarios are considered. A characteristic function of the n -person cooperative game with multiple scenarios associates a subset of the set of all players with its real vector value. We consider the nucleolus, which is one of solution concepts based on the lexicographical framework in an n -person cooperative game, in the game with multiple scenarios. To define extended nucleoli, three aggregation methods using weighting coefficients, a minimum component, and constraints are employed. The computational methods for the three extended nucleoli are developed by repeatedly solving linear programming problems. Finally, a numerical example illustrates the proposed methods.