Application of STP to cooperative games

Using semi-tensor product (STP) of matrices, a characteristic function is converted into a pseudo-Boolean function. In the light of this form, two fundamental formulas in cooperative game theory have been simplified. First, the coefficient formula for a game to be expressed as a linear combination of unanimity games is obtained. Second, a novel formula is proposed to calculate Shapley value. These two formulas are simple. They can not only reduce the computational complexity but also be used in theoretical analysis. The STP is introduced in the appendix.