Consolidation of an Efficient and a Non-Efficient Solution in a Cooperative Game: The Egalitarian Banzhaf Value

Abstract

Objective: The principles of marginalism and egalitarianism are handy tools for sharing worth among the players of a group in a TU game. Here, our objective is to combine two such solutions to generate a new value that keeps in mind the need of each player required for the survival of a group in a TU game. Methods: Here, the Banzhaf value and the equal division value were merged to establish a new consolidated solution. Method of induction is used over unanimity games and symmetric games to characterize the proposed value using some well-known as well as some freshly defined axioms of cooperative game theory. Findings: To describe the new value, we first looked at a number of intuitive axioms linked to it and the uniqueness of the value is obtained by characterizing it using the defined axioms. The value is then extended to the class of simple games. Novelty: The proposed solution is a non-efficient solution that allocates a portion of the total worth to the players and keeps a portion undistributed to use for the purpose of further investment by the group. Keywords: Cooperative game; Banzhaf value; Egalitarian Value; Null Player; Solution Concept