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Compromising between the proportional and equal division values: axiomatization, consistency and implementation

Author

Listed:
  • Zhengxing Zou

    (Beijing Jiaotong University)

  • Rene van den Brink

    (Vrije Universiteit Amsterdam)

  • Yukihiko Funaki

    (Waseda University Tokyo)

Abstract

We introduce a family of values for TU-games that offers a compromise between the proportional and equal division values. Each value, called an alpha-mollified value, is obtained in two steps. First, a linear function with respect to the worths of all coalitions is defined which associates a real number to every TU-game. Second, the weight assigned by this function is used to weigh proportionality and equality principles in allocating the worth of the grand coalition. We provide an axiomatic characterization of this family, and show that this family contains the affine combinations of the equal division value and the equal surplus division value as the only linear values. Further, we identify the proportional division value and the affine combinations of the equal division value and the equal surplus division value as those members of this family, that satisfy projection consistency. Besides, we provide a procedural implementation of each single value in this family.

Suggested Citation

  • Zhengxing Zou & Rene van den Brink & Yukihiko Funaki, 2020. "Compromising between the proportional and equal division values: axiomatization, consistency and implementation," Tinbergen Institute Discussion Papers 20-054/II, Tinbergen Institute.
    • Handle: RePEc:tin:wpaper:20200054
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    References listed on IDEAS

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    1. Zhengxing Zou & René Brink & Youngsub Chun & Yukihiko Funaki, 2021. "Axiomatizations of the proportional division value," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 57(1), pages 35-62, July.
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    More about this item

    Keywords

    Cooperative game; consistency; equal division value; proportional division value;
    All these keywords.

    JEL classification:

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

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