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Null, Nullifying, and Necessary Agents: Parallel Characterizations of the Banzhaf and Shapley Values

Author

Listed:
  • José M. Alonso-Meijide

    (Universidade de Santiago de Compostela)

  • Julián Costa

    (Universidade da Coruña)

  • Ignacio García-Jurado

    (Universidade da Coruña)

Abstract

In a cooperative game, we consider three special kinds of agents: null, nullifying, and necessary agents. A coalition with a null agent receives the same payoff if this agent leaves the coalition, a coalition with a nullifying agent receives nothing, and a coalition without a necessary agent also receives nothing. The null agent property proposes zero payoff to any null agent. We introduce new properties that propose payoffs for nullifying and necessary players. With these three properties and additivity, we obtain new characterizations of the Banzhaf and Shapley values.

Suggested Citation

  • José M. Alonso-Meijide & Julián Costa & Ignacio García-Jurado, 2019. "Null, Nullifying, and Necessary Agents: Parallel Characterizations of the Banzhaf and Shapley Values," Journal of Optimization Theory and Applications, Springer, vol. 180(3), pages 1027-1035, March.
    • Handle: RePEc:spr:joptap:v:180:y:2019:i:3:d:10.1007_s10957-018-1403-5
    DOI: 10.1007/s10957-018-1403-5
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    References listed on IDEAS

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    3. Kamijo, Yoshio & Kongo, Takumi, 2012. "Whose deletion does not affect your payoff? The difference between the Shapley value, the egalitarian value, the solidarity value, and the Banzhaf value," European Journal of Operational Research, Elsevier, vol. 216(3), pages 638-646.
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    Cited by:

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    2. Jun Su & Yuan Liang & Guangmin Wang & Genjiu Xu, 2020. "Characterizations, Potential, and an Implementation of the Shapley-Solidarity Value," Mathematics, MDPI, vol. 8(11), pages 1-20, November.
    3. 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.

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