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Weak null, necessary defender and necessary detractor players: characterizations of the Banzhaf and the Shapley bisemivalues

Author

Listed:
  • Margarita Domènech

    (Technical University of Catalonia)

  • José Miguel Giménez

    (Technical University of Catalonia)

  • María Albina Puente

    (Technical University of Catalonia)

Abstract

We focus on bicooperative games, a variation of the classic cooperative games and, in particular, on the Banzhaf and the Shapley bisemivalues defined on these games. We consider three special classes of players: weak null, necessary defender and necessary detractor players. By introducing new properties related to this kind of players, we provide new axiomatic characterizations of the Banzhaf and the Shapley bisemivalues giving, in both cases, a set of independent properties that univocally determine them. We also provide a computational procedure to calculate the allocations given by the Shapley bisemivalue in terms of the generalized multilinear extension of the game.

Suggested Citation

  • Margarita Domènech & José Miguel Giménez & María Albina Puente, 2022. "Weak null, necessary defender and necessary detractor players: characterizations of the Banzhaf and the Shapley bisemivalues," Annals of Operations Research, Springer, vol. 318(2), pages 889-910, November.
    • Handle: RePEc:spr:annopr:v:318:y:2022:i:2:d:10.1007_s10479-021-04153-6
    DOI: 10.1007/s10479-021-04153-6
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    References listed on IDEAS

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