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Coalitional desirability and the equal division value

Author

Listed:
  • Sylvain Béal

    (Univ. Bourgogne Franche-Comté)

  • Eric Rémila

    (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne)

  • Philippe Solal

    (Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne)

Abstract

We introduce three natural collective variants of the well-known axiom of desirability (Maschler and Peleg in Pac J Math 18:289–328, 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 & Philippe Solal, 2019. "Coalitional desirability and the equal division value," Theory and Decision, Springer, vol. 86(1), pages 95-106, February.
    • Handle: RePEc:kap:theord:v:86:y:2019:i:1:d:10.1007_s11238-018-9672-x
    DOI: 10.1007/s11238-018-9672-x
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    4. Hu, Xun-Feng, 2019. "Coalitional surplus desirability and the equal surplus division value," Economics Letters, Elsevier, vol. 179(C), pages 1-4.
    5. 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.

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