A Further Research on S-core for Interval Cooperative Games

Interval cooperative game is a kind of model focusing on how to distribute the profit reasonably when payoffs of any alliance are interval numbers. In recent years, the existence and reasonableness of its solution have aroused widespread concern. In this paper, based on the conceptual analyses of various solutions of interval cooperative games, S-core is further researched. The concepts of weak balanced interval cooperative games and minimal weak balanced interval cooperative games are firstly proposed. The necessary and sufficient condition which guarantees S-core is nonempty is proven, furthermore, the inequalities can be simplified on the condition that the left endpoints of interval numbers satisfy the superadditivity. Then this paper analyzes the whole solution space of S-core and the solution method of S-core is converted into the method solving a linear programming problem. After that the concept of S-dominance core is put forward and the equivalent conditions of S-core and S-dominance core are proved. Finally, the reasonableness and validity of S-core are verified through a specific example.