Balanced externalities and the Shapley value

Shapley Value for Games with Externalities and Games on Graphs

The Shapley value [46] is one of the most important solution concepts in coalitional game theory. It was originally defined for classical model of a coalitional game, which is relevant to a wide range of economic and social situations. However, while in certain cases the simplicity is the strength of the classical coalitional game model, it often becomes a limitation. To address this problem, a...

Marginality Approach To Shapley Value In Games With Externalities

The extended and generalized Shapley value: Simultaneous consideration of coalitional externalities and coalitional structure

The Shapley value assigns, to each game that is adequately represented by its characteristic function, an outcome for each player. An elaboration on the Shapley value that assigns, to characteristic function games, a “partition function”outcome is broadly established and accepted, but elaborations to encompass games with externalities (represented by partition functions) are not. Here, I show t...

Sharing the surplus: An extension of the Shapley value for environments with externalities

Economic activities, both on the macro and micro level, often entail wide-spread externalities. This in turn leads to disputes regarding the compensation levels to the various parties affected. We propose a method of deciding upon the distribution of the gains (costs) of cooperation in the presence of externalities when forming the grand coalition is efficient. We show that any sharing rule sat...

The Marginality Approach for the Shapley Value in Games with Externalities

One of the long-debated issues in coalitional game theory is how to extend the Shapley to games with externalities (partition-function games). When externalities are present, not only can a player’s marginal contribution to a coalition—a central notion to the Shapley value—be defined in a variety of ways, but it is also not obvious which axiomatization should be used. Consequently, a number of ...