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Coalitional desirability and the equal division value

Author

Listed:
  • Sylvain Béal

    (Université de Bourgogne Franche-Comté, CRESE)

  • Eric Rémila

    (Université de Saint-Etienne, Gate)

  • Phillippe Solal

    (Université de Saint-Etienne, Gate)

Abstract
We introduce three natural collective variants of the well-known axiom of Desirability (Maschler and Peleg, 1966), which require that if the (per capita) contributions of a first coalition are at least as large as the (per capita) contributions of a second coalition, then the (average) payoff in the first coalition should be as large as the (average) payoff in the second coalition. These axioms are called Coalitional desirability and Average coalitional desirability. The third variant, called Uniform coalitional desirability applies only to coalitions with the same size. We show that Coalitional desirability is very strong: no value satisfies simultaneously this axiom and Efficiency. To the contrary, the combination of either Average coalitional desirability or Uniform coalitional desirability with Efficiency and Additivity characterizes the Equal Division value.

Suggested Citation

  • Sylvain Béal & Eric Rémila & Phillippe Solal, 2017. "Coalitional desirability and the equal division value," Working Papers 2017-08, CRESE.
    • Handle: RePEc:crb:wpaper:2017-08
    DOI: https://doi.org/10.1007/s11238-018-9672-x
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    References listed on IDEAS

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    Cited by:

    1. Hu, Xun-Feng, 2019. "Coalitional surplus desirability and the equal surplus division value," Economics Letters, Elsevier, vol. 179(C), pages 1-4.
    2. J. M. Alonso-Meijide & J. Costa & I. García-Jurado & J. C. Gonçalves-Dosantos, 2020. "On egalitarian values for cooperative games with a priori unions," TOP: An Official Journal of the Spanish Society of Statistics and Operations Research, Springer;Sociedad de Estadística e Investigación Operativa, vol. 28(3), pages 672-688, October.
    3. Koji Yokote & Takumi Kongo & Yukihiko Funaki, 2021. "Redistribution to the less productive: parallel characterizations of the egalitarian Shapley and consensus values," Theory and Decision, Springer, vol. 91(1), pages 81-98, July.
    4. Lina Mallozzi & Juan Vidal-Puga, 2021. "Uncertainty in cooperative interval games: how Hurwicz criterion compatibility leads to egalitarianism," Annals of Operations Research, Springer, vol. 301(1), pages 143-159, June.
    5. Sylvain Béal & Florian Navarro, 2020. "Necessary versus equal players in axiomatic studies," Post-Print hal-03252179, HAL.

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    More about this item

    Keywords

    Desirability; Coalitional desirability; Average coalitional desirability; Uniform coalitional desirability; Equal Division value; Shapley value.;
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