Steady Marginality: A Uniform Approach to Shapley Value for Games with Externalities

Abstract

The Shapley value is one of the most important solution concepts in cooperative game theory. In coalitional games without externalities, it allows to compute a unique payoff division that meets certain desirable fairness axioms. However, in many realistic applications where are present, Shapley's axioms fail to indicate such a unique division. Consequently, there are many extensions of Shapley value to the environment with proposed in the literature built upon additional axioms. Two important such extensions are externality-free value by Pham Do and Norde and value that absorbed all externalities by McQuillin. They are good reference points in a space of potential payoff divisions for coalitional games with as they limit the space at two opposite extremes. In a recent, important publication, De Clippel and Serrano presented a marginality-based axiomatization of the value by Pham Do Norde. In this paper, we propose a dual approach to marginality which allows us to derive the value of McQuillin. Thus, we close the picture outlined by De Clippel and Serrano.