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Compromise for the Per Capita Complaint: An Optimization Characterization of Two Equalitarian Values


  • Dongshuang Hou

    (Department of Applied Mathematics, Northwestern Polytechnical University)

  • Aymeric Lardon

    (Université Côte d'Azur, France

  • Panfei Sun

    (Department of Applied Mathematics, Northwestern Polytechnical University)

  • Theo Driessen

    (Department of Applied Mathematics, University of Twente, The Netherlands)


The main purpose of this article is to introduce two new values for transferable utility (TU) games: the upper and lower optimal complaint values. These are based on two kinds of per capita complaint criteria and each involve a lower and upper bound of the core. In the spirit of the nucleolus, these two values are obtained by lexicographically minimizing a maximal complaint vector associated with each of the per capita complaint criterion. Interestingly, the upper and lower optimal complaint values respectively coincide with the Equal Allocation of Non-Separable Contributions and the Center-of-Gravity of Imputation Set Value for a large class of TU-games. Moreover, a characterization of these two values is achieved by invoking the equal upper and lower maximal per capita complaint properties together with efficiency.

Suggested Citation

  • Dongshuang Hou & Aymeric Lardon & Panfei Sun & Theo Driessen, 2018. "Compromise for the Per Capita Complaint: An Optimization Characterization of Two Equalitarian Values," GREDEG Working Papers 2018-13, Groupe de REcherche en Droit, Economie, Gestion (GREDEG CNRS), Université Côte d'Azur, France.
  • Handle: RePEc:gre:wpaper:2018-13

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    References listed on IDEAS

    1. Oishi, Takayuki & Nakayama, Mikio & Hokari, Toru & Funaki, Yukihiko, 2016. "Duality and anti-duality in TU games applied to solutions, axioms, and axiomatizations," Journal of Mathematical Economics, Elsevier, vol. 63(C), pages 44-53.
    2. Moulin, Herve, 1985. "The separability axiom and equal-sharing methods," Journal of Economic Theory, Elsevier, vol. 36(1), pages 120-148, June.
    3. Yan-An Hwang, 2006. "Associated consistency and equal allocation of nonseparable costs," Economic Theory, Springer;Society for the Advancement of Economic Theory (SAET), vol. 28(3), pages 709-719, August.
    4. Sylvain Béal & Eric Rémila & Philippe Solal, 2016. "Characterizations of Three Linear Values for TU Games by Associated Consistency: Simple Proofs Using the Jordan Normal Form," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 18(01), pages 1-21, March.
    5. Huijink, S. & Borm, P.E.M. & Kleppe, J. & Reijnierse, J.H., 2015. "Bankruptcy and the per capita nucleolus: The claim-and-right rules family," Mathematical Social Sciences, Elsevier, vol. 77(C), pages 15-31.
    6. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," CORE Discussion Papers RP 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    7. Sylvain Béal & Marc Deschamps & Philippe Solal, 2016. "Comparable Axiomatizations of Two Allocation Rules for Cooperative Games with Transferable Utility and Their Subclass of Data Games," Journal of Public Economic Theory, Association for Public Economic Theory, vol. 18(6), pages 992-1004, December.
    8. Huijink, S. & Borm, P.E.M. & Reijnierse, J.H. & Kleppe, J., 2013. "Bankruptcy and the Per Capita Nucleolus," Discussion Paper 2013-059, Tilburg University, Center for Economic Research.
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    More about this item


    Cooperative game; optimal complaint values; equalitarian values; equal maximal per capita complaint properties;

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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