Power surplus solutions for weighted hypergraph communication situations

In this paper, we study a framework of weighted hypergraph communication situations, in which each hyperlink is interpreted as a conference and the same players may have different weights in different conferences. Since common players play an intermediary role in the communication between conferences for hypergraph communication situations, we believe that noncommon players should pay a certain fee to the common players as an intermediary fee, and accordingly propose a concept of power index. We define and characterize so-called power surplus solutions for weighted acyclic hypergraph communication situations, which distribute the surplus of each conference based on the power index of its members. Finally, two applications of power surplus solutions are discussed.