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Value dividends, the Harsanyi set and extensions, and the proportional Harsanyi solution

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  • Manfred Besner

    (University of Applied Sciences)

Abstract

A new concept for TU-values, called value dividends, is introduced. Similar to Harsanyi dividends, value dividends are defined recursively and provide new characterizations of values from the Harsanyi set. In addition, we generalize the Harsanyi set where each of the TU-values from this set is defined by the distribution of the Harsanyi dividends via sharing function systems and give an axiomatic characterization. As a TU value from the generalized Harsanyi set, we present the proportional Harsanyi solution, a new proportional solution concept. A new characterization of the Shapley value is proposed as a side effect. None of our characterizations uses additivity.

Suggested Citation

  • Manfred Besner, 2020. "Value dividends, the Harsanyi set and extensions, and the proportional Harsanyi solution," International Journal of Game Theory, Springer;Game Theory Society, vol. 49(3), pages 851-873, September.
    • Handle: RePEc:spr:jogath:v:49:y:2020:i:3:d:10.1007_s00182-019-00701-4
    DOI: 10.1007/s00182-019-00701-4
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    References listed on IDEAS

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    Cited by:

    1. Besner, Manfred, 2022. "Impacts of boycotts concerning the Shapley value and extensions," MPRA Paper 112620, University Library of Munich, Germany.
    2. Besner, Manfred, 2022. "The grand surplus value and repeated cooperative cross-games with coalitional collaboration," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    3. Besner, Manfred, 2020. "Values for level structures with polynomial-time algorithms, relevant coalition functions, and general considerations," MPRA Paper 99355, University Library of Munich, Germany.
    4. Besner, Manfred, 2021. "The grand dividends value," MPRA Paper 107615, University Library of Munich, Germany.
    5. Zhengxing Zou & René Brink & Yukihiko Funaki, 2022. "Sharing the surplus and proportional values," Theory and Decision, Springer, vol. 93(1), pages 185-217, July.
    6. 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.
    7. Besner, Manfred, 2021. "Disjointly productive players and the Shapley value," MPRA Paper 108241, University Library of Munich, Germany.
    8. Besner, Manfred, 2021. "The grand dividends value," MPRA Paper 106638, University Library of Munich, Germany.
    9. David Lowing & Makoto Yokoo, 2023. "Sharing values for multi-choice games: an axiomatic approach," Working Papers hal-04018735, HAL.
    10. Besner, Manfred, 2022. "Disjointly productive players and the Shapley value," Games and Economic Behavior, Elsevier, vol. 133(C), pages 109-114.
    11. Besner, Manfred, 2022. "Impacts of boycotts concerning the Shapley value and extensions," Economics Letters, Elsevier, vol. 217(C).
    12. Zou, Zhengxing & van den Brink, René & Funaki, Yukihiko, 2021. "Compromising between the proportional and equal division values," Journal of Mathematical Economics, Elsevier, vol. 97(C).
    13. Surajit Borkotokey & Sujata Gowala & Rajnish Kumar, 2023. "The Expected Shapley value on a class of probabilistic games," Papers 2308.03489, arXiv.org.
    14. Besner, Manfred, 2021. "Disjointly and jointly productive players and the Shapley value," MPRA Paper 108511, University Library of Munich, Germany.

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