A method to compare the coalition influence and a evaluation function based on profitability of coalition in games in characteristic function form

This paper proposes a binary relation to compare coalition influence and a function which assigns a real number which expresses potential profitability that a coalition has to the coalition in the framework of games in characteristic function form. Some examples how the proposed binary relation and the function in games in characteristic function form are provided. The authors give some propositions which the proposed method and the function satisfy.