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Cohesive efficiency in TU-games: axiomatizations of variants of the Shapley value, egalitarian values and their convex combinations

Abstract

We relax the assumption that the grand coalition must form by imposing the axiom of Cohesive efficiency: the total payoffs that the players can share is equal to the maximal total worth generated by a coalition structure. We determine how the three main axiomatic characterizations of the Shapley value are affected when the classical axiom of Efficiency is replaced by Cohesive efficiency. We introduce and characterize two variants of the Shapley value that are compatible with Cohesive efficiency. We show that our approach can also be applied to the variants of more egalitarian values.

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Notes

  1. Note that differential marginality is equivalent to the fairness property suggested by van den Brink (2001) as shown by Casajus, (2011), Proposition 3).

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Correspondence to Sylvain Béal.

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We thank Walter Trockel and two anonymous reviewers for useful remarks. Financial support from research programs IDEXLYON from Université de Lyon (project INDEPTH) within the Programme Investissements d’Avenir (ANR-16-IDEX-0005), and “Mathématiques de la décision pour l’ingénierie physique et sociale” (MODMAD) is gratefully acknowledged by the first, third and fourth authors. The second author is funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—388390901.

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Béal, S., Casajus, A., Rémila, E. et al. Cohesive efficiency in TU-games: axiomatizations of variants of the Shapley value, egalitarian values and their convex combinations. Ann Oper Res 302, 23–47 (2021). https://doi.org/10.1007/s10479-021-04005-3

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  • DOI: https://doi.org/10.1007/s10479-021-04005-3

Keywords

  • Cohesive efficiency
  • Shapley value
  • Balanced contributions
  • Potential
  • Equal (surplus) division
  • Equal allocation of nonseparable costs
  • Consensus values
  • Egalitarian Shapley values
  • Superadditive cover