DMMP Seminar

Yuan Feng — A Matrix Approach to the Associated Consistency of the Generalized Shapley Value

We focus on the Shapley value for cooperative games in generalized characteristic function form, in which the players of coalitions are supposed to be ordered. An axiomatization of the generalized Shapley value is presented in terms of three properties, namely continuity, associated consistency, and inessential game property. The proof technique is based on fundamental matrix representations and the Diagonal Theorem for matrices. The rank, eigenvalues and eigenvectors for a certain representation matrix are treated to guarantee the application of the diagonalization.