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The family of lattice structure values for games with externalities

Author

Listed:
  • José Mª Alonso-Meijide

    (Universidade de Santaigo de Compostela)

  • Mikel Alvarez-Mozos

    (Universitat de Barcelona)

  • Mª Gloria Fiestras-Janeiro

    (Universidade de Vigo)

  • Andrés Jiménez-Losada

    (Universidad de Sevilla)

Abstract

We propose and characterize a new family of Shapley values for games with coalitional externalities. To define it we generalize the concept of marginal contribution by using a lattice structure on the set of embedded coalitions. The family of lattice structure values is characterized by extensions of Shapley's axioms: efficiency, additivity, symmetry, and the null player property. The first three axioms have widely accepted generalizations to the framework of games with externalities. However, different concepts of null players have been proposed in the literature and we contribute to this debate with a new one. The null player property that we use is weaker than the others. Finally, we present one particular value of the family, new in the literature, which delivers balanced payoffs and characterize it by two additional properties.

Suggested Citation

  • José Mª Alonso-Meijide & Mikel Alvarez-Mozos & Mª Gloria Fiestras-Janeiro & Andrés Jiménez-Losada, 2018. "The family of lattice structure values for games with externalities," UB School of Economics Working Papers 2018/379, University of Barcelona School of Economics.
    • Handle: RePEc:ewp:wpaper:379web
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    File URL: http://hdl.handle.net/2445/124420
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    More about this item

    Keywords

    Externalities; Partition function; Basis; Lattice; Marginal contribution.;
    All these keywords.

    JEL classification:

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

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