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From hierarchies to levels: new solutions for games with hierarchical structure

Author

Listed:
  • M. Álvarez-Mozos

    (Universitat de Barcelona)

  • R. Brink

    (VU Amsterdam)

  • G. Laan

    (VU Amsterdam)

  • O. Tejada

    () (ETH Zurich)

Abstract

Abstract Recently, applications of cooperative game theory to economic allocation problems have gained popularity. In many of these problems, players are organized according to either a hierarchical structure or a levels structure that restrict the players’ possibilities to cooperate. In this paper, we propose three new solutions for games with hierarchical structure and characterize them by properties that relate a player’s payoff to the payoffs of other players located in specific positions in the hierarchical structure relative to that player. To define each solution, we consider a certain mapping that transforms the hierarchical structure into a levels structure, and then we apply the standard generalization of the Shapley value to the class of games with levels structure. Such transformation mappings are studied by means of properties that relate a player’s position in both types of structure.

Suggested Citation

  • M. Álvarez-Mozos & R. Brink & G. Laan & O. Tejada, 2017. "From hierarchies to levels: new solutions for games with hierarchical structure," International Journal of Game Theory, Springer;Game Theory Society, vol. 46(4), pages 1089-1113, November.
  • Handle: RePEc:spr:jogath:v:46:y:2017:i:4:d:10.1007_s00182-017-0572-z
    DOI: 10.1007/s00182-017-0572-z
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    References listed on IDEAS

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    Cited by:

    1. Besner, Manfred, 2018. "The weighted Shapley support levels values," MPRA Paper 87617, University Library of Munich, Germany.
    2. Besner, Manfred, 2017. "Weighted Shapley levels values," MPRA Paper 82978, University Library of Munich, Germany.

    More about this item

    Keywords

    TU-game; Hierarchical structure; Levels structure; Shapley value; Axiomatization;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C70 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - General

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