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

Author

Listed:
  • Dongshuang Hou

    (Department of Applied Mathematics, Northwestern Polytechnical University)

  • Aymeric Lardon

    (Université Côte d'Azur, France
    GREDEG CNRS)

  • Panfei Sun

    (Department of Applied Mathematics, Northwestern Polytechnical University)

  • Theo Driessen

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

Abstract

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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    File URL: http://195.220.198.217/GREDEG-WP-2018-13.pdf
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    References listed on IDEAS

    as
    1. 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.
    2. SCHMEIDLER, David, 1969. "The nucleolus of a characteristic function game," LIDAM Reprints CORE 44, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    3. Huijink, S. & Borm, P.E.M. & Reijnierse, J.H. & Kleppe, J., 2013. "Bankruptcy and the Per Capita Nucleolus," Other publications TiSEM 0b1d187b-a251-47c0-92d8-7, Tilburg University, School of Economics and Management.
    4. 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.
    5. 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.
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    More about this item

    Keywords

    Cooperative game; optimal complaint values; equalitarian values; equal maximal per capita complaint properties;
    All these keywords.

    JEL classification:

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

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