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

  • Oskar Skibski
Part of the Lecture Notes in Computer Science book series (LNCS, volume 6982)


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.


Marginal Contribution Grand Coalition Coalitional Game Cooperative Game Theory Axiomatic Characterization 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Oskar Skibski
    • 1
  1. 1.Institute of InformaticsUniversity of WarsawWarsawPoland

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