An Equivalent Formulation for the Shapley Value

  • Josep FreixasEmail author
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11290)


An equivalent explicit formula for the Shapley value is provided, its equivalence with the classical one is proven by double induction. The importance of this new formula, in contrast to the classical one, is its capability of being extended to more general classes of games, in particular to j-cooperative games or multichoice games, in which players choose among different levels of participation in the game.


Cooperative games Marginal contributions Shapley value Alternative formulations Potential generalizations 



This author research was partially supported by funds from the Spanish Ministry of Economy and Competitiveness (MINECO) and from the European Union (FEDER funds) under grant MTM2015-66818-P (MINECO/FEDER).

The author is grateful for the comments of two reviewers who have helped to improve the work.


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Universitat Politècnica de Catalunya (Campus Manresa i Departament de Matemàtiques)ManresaSpain

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