The generalized symmetric coalitional Banzhaf value for multichoice games with a coalition structure

Abstract

With respect to multichoice games with a coalition structure, a coalitional value named the generalized symmetric coalitional Banzhaf value is defined, which is an extension of the Shapley value for multichoice games and the symmetric coalitional Banzhaf value for traditional games with a coalition structure. Two axiomatic systems are established: One is enlightened by the characterizations for the symmetric coalitional Banzhaf value, and the other is inspired by the characterizations for the Banzhaf value.

A coalitional value for games on convex geometries with a coalition structure

“…The axiomatic systems for the Owen value are researched by Albizuri [19], Hamiache [20] and Khmelnitskaya and Yanovskaya [21], whilst the characterizations of the Banzhaf-Owen value are discussed by Amer et al [22] and Alonso-Meijide et al [23]. Furthermore, multi-choice games with a coalition structure are considered in [24][25][26].…”