On an axiomatization of the grey Banzhaf value

Abstract

The Banzhaf value with grey data is a solution concept in cooperative grey games that has been extensively studied in the context of operations research. The author aims to define the traits of the Banzhaf value in cooperative grey games, where the values of coalitions are depicted as grey numbers within intervals. The grey Banzhaf value is defined by several axioms, including the grey dummy player, grey van den Brink fairness, and grey superadditivity. By presenting these axioms, this investigation contributes novel insights to the axiomatic characterization of the grey Banzhaf value, offering a distinct perspective. Finally, the study concludes by presenting applications in cooperative grey game models, thereby enriching the understanding of this concept.

Keywords

• banzhaf value
• grey calculus
• cooperative grey games
• shapley value
• characterization