Steady Marginality: A Uniform Approach to Shapley Value for Games with Externalities
نویسنده
چکیده
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 extensions of Shapley value to the environment with externalities 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 externalities 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.
منابع مشابه
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 ...
متن کاملAn axiomatic characterization of a value for games in partition function form
An extension of the Shapley value for games in partition function form is proposed in the paper. We introduce a version of the marginal contributions for environments with externalities. The dummy property related to it is defined. We adapt the system of axioms provided by Shapley (A value for n-Person games. In: Kuhn H, Tucker A (eds) Contributions to the theory of games II. Princeton Universi...
متن کاملWeak 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 ...
متن کاملCooperative Benefit and Cost Games under Fairness Concerns
Solution concepts in cooperative games are based on either cost games or benefit games. Although cost games and benefit games are strategically equivalent, that is not the case in general for solution concepts. Motivated by this important observation, a new property called invariance property with respect to benefit/cost allocation is introduced in this paper. Since such a property can be regar...
متن کامل