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Coalitional desirability and the equal division value

Author

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  • Sylvain Béal

    () (CRESE - Centre de REcherches sur les Stratégies Economiques (EA 3190) - UBFC - Université Bourgogne Franche-Comté [COMUE] - UFC - Université de Franche-Comté)

  • Éric Rémila

    () (GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - ENS Lyon - École normale supérieure - Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet [Saint-Étienne] - Université de Lyon - CNRS - Centre National de la Recherche Scientifique)

  • Philippe Solal

    (GATE Lyon Saint-Étienne - Groupe d'analyse et de théorie économique - ENS Lyon - École normale supérieure - Lyon - UL2 - Université Lumière - Lyon 2 - UCBL - Université Claude Bernard Lyon 1 - Université de Lyon - UJM - Université Jean Monnet [Saint-Étienne] - Université de Lyon - CNRS - Centre National de la Recherche Scientifique)

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.
(This abstract was borrowed from another version of this item.)

Suggested Citation

  • Sylvain Béal & Éric Rémila & Philippe Solal, 2019. "Coalitional desirability and the equal division value," Post-Print halshs-01951010, HAL.
  • Handle: RePEc:hal:journl:halshs-01951010
    Note: View the original document on HAL open archive server: https://halshs.archives-ouvertes.fr/halshs-01951010
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    References listed on IDEAS

    as
    1. Sylvain Béal & Eric Rémila & Philippe Solal, 2015. "Axioms of invariance for TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(4), pages 891-902, November.
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    1. repec:eee:ecolet:v:179:y:2019:i:c:p:1-4 is not listed on IDEAS
    2. Mallozzi, Lina & Vidal-Puga, Juan, 2019. "Uncertainty in cooperative interval games: How Hurwicz criterion compatibility leads to egalitarianism," MPRA Paper 92730, University Library of Munich, Germany.

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