Marginality Approach to Shapley Value in Games with Externalities

Marginality Approach To Shapley Value In Games With Externalities

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

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 externalities are present, Shapley’s axioms fail to indicate such a unique division. Consequently, there are many extensio...

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 ...

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...

Weak differential marginality and the Shapley value

The principle of differential marginality for cooperative games states that the differential of two players’ payoffs does not change when the differential of these players’ productivities does not change. Together with two standard properties, efficiency and the null player property, differential marginality characterizes the Shapley value. For games that contain more than two players, we show ...