The Unique Characterization of the Shapley Value for Bi-cooperative Games

Abstract

The aim of the present paper is to study the unique characterization for bicooperative games. Shapley value is the expected marginal contribution of the alliance. We will introduce some properties for bicooperative games. Our first characterization is based on the classical axioms determining the Shapley value with the symmetry axiom replaced excluded null axiom. In our second axiomatization we use structural axiom and a zero excluded axiom instead of effective axiom in classical cooperative games. Finally, We provide here linearity, anonymity, dummy and efficiency and structural axioms to study a one-point solution concept for Bi-cooperative games.