96 research outputs found
Marginal contributions and externalities in the value
For games in partition function form, we explore the implications of distinguishing between the concepts of intrinsic marginal contributions and externalities. If one requires efficiency for the grand coalition, we provide several results concerning extensions of the Shapley value. Using the axioms of efficiency, anonymity, marginality and monotonicity, we provide upper and lower bounds to players' payoffs when affected by external effects, and a characterization of an ''externality-free'' value. If the grand coalition does not form, we characterize a payoff configuration on the basis of the principle of balanced contributions. We also analyze a game of coalition formation that yields sharp prediction
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 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
- …