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Coalitional desirability and the equal division value

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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.

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Notes

  1. The results in this note are still valid if this assumption is relaxed in the definition of our new axioms.

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Authors and Affiliations

  1. CRESE EA3190, Univ. Bourgogne Franche-Comté, 25000, Besançon, France

    Sylvain Béal

  2. Université de Saint-Etienne, CNRS UMR 5824 GATE Lyon Saint-Etienne, Saint-Étienne, France

    Eric Rémila & Philippe Solal

Authors
  1. Sylvain Béal
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  2. Eric Rémila
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  3. Philippe Solal
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Correspondence to Sylvain Béal.

Additional information

We would like to thank an associate editor and two reviewers for valuable comments. Financial support from research programs “DynaMITE: Dynamic Matching and Interactions: Theory and Experiments”, contract ANR-13-BSHS1-0010, INDEPTH and “Mathématiques de la décision pour l’ingénierie physique et sociale” (MODMAD) is gratefully acknowledged.

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Béal, S., Rémila, E. & Solal, P. Coalitional desirability and the equal division value. Theory Decis 86, 95–106 (2019). https://doi.org/10.1007/s11238-018-9672-x

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