The Interval Core of the Minimum Cost Spanning Tree Interval Game and Its Calculation

In this paper, the minimal cost spanning tree interval game is studied. It is proved that the interval core is no empty when n=2. By introducing the concepts of the left game, right game of MCSTIG, and compositive, it is proved there exists a hyperplane with non-negative normal vector to separate L and R strictly. when the interval core of MCSTIG is empty. It obtained the sufficient and necessary condition of no empty interval core of MCSTIG, by using linear programming tools. Finally, the algorithm to calculate the interval core of MCSTIG is presented.