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Values on regular games under Kirchhoff's laws

Author

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  • Fabien Lange

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, Keleti Faculty of Economics - Budapest Tech)

  • Michel Grabisch

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

Abstract

The Shapley value is a central notion defining a rational way to share the total worth of a cooperative game among players. We address a general framework leading to applications to games with communication graphs, where the feasible coalitions form a poset whose all maximal chains have the same length. Considering a new way to define the symmetry among players, we propose an axiomatization of the Shapley value of these games. Borrowing ideas from electric networks theory, we show that our symmetry axiom and the efficiency axiom correspond to the two Kirchhoff's laws in the circuit associated to the Hasse diagram of feasible coalitions.

Suggested Citation

  • Fabien Lange & Michel Grabisch, 2009. "Values on regular games under Kirchhoff's laws," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00496553, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00496553
    DOI: 10.1016/j.mathsocsci.2009.07.003
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00496553v1
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    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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