On connections between individual values and coalition values for games in characteristic function form

Abstract

This paper investigates some connections between individual values, such as the Shapley value and the Banzhaf value, and coalition values, such as blockability value, viability value and profitability value, for games in characteristic function form. It turns out that the Shapley value, the Banzhaf value, blockability value, viability value and profitability value assign the same real number to each coalition where the characteristic function is superadditive and inessential. It is also clarified that there is equalization of the Banzhaf value and profitability value of each player in constant-sum game. A new class of games in characteristic function form, which is called equally average coalition solidarity, is proposed in this paper. A proposition which shows that every player’s real number evaluated by the Shapley value corresponds with the real number evaluated by the Banzhaf value of the player in the proposed class of games in characteristic function form is provided.