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Equivalent Representations of a Set Function with Applications to Game Theory and Multicriteria Decision Making

Author

Listed:
  • Grabisch, M.
  • Marichal, J.-L.
  • Roubens, M.

Abstract

This paper introduces four alternative representations of a set function: the Mobius transformation, the co-Mobius transformation, and the interactions between elements of any subset of a given set as extensions of Shapley and Banzhaf values. The links between the five equivalent representations of a set function are emphasized in this presentation.

Suggested Citation

  • Grabisch, M. & Marichal, J.-L. & Roubens, M., 1998. "Equivalent Representations of a Set Function with Applications to Game Theory and Multicriteria Decision Making," Liege - Groupe d'Etude des Mathematiques du Management et de l'Economie 9801, UNIVERSITE DE LIEGE, Faculte d'economie, de gestion et de sciences sociales, Groupe d'Etude des Mathematiques du Management et de l'Economie.
  • Handle: RePEc:fth:gemame:9801
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    Citations

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    Cited by:

    1. Fabien Lange & Michel Grabisch, 2006. "Interaction transform for bi-set functions over a finite set," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00186891, HAL.
    2. Fabien Lange & László Kóczy, 2013. "Power indices expressed in terms of minimal winning coalitions," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 41(2), pages 281-292, July.

    More about this item

    Keywords

    GAME THEORY ; DECISION MAKING;

    JEL classification:

    • C60 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - General
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

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