IDEAS home Printed from https://ideas.repec.org/p/pra/mprapa/92247.html
   My bibliography  Save this paper

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

Author

Listed:
  • Besner, Manfred

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 payoff, a new proportional solution concept. As a side benefit, a new characterization of the Shapley value is proposed. None of our characterizations uses additivity.

Suggested Citation

  • Besner, Manfred, 2019. "Value dividends, the Harsanyi set and extensions, and the proportional Harsanyi payoff," MPRA Paper 92247, University Library of Munich, Germany.
    • Handle: RePEc:pra:mprapa:92247
    as

    Download full text from publisher

    File URL: https://mpra.ub.uni-muenchen.de/92247/1/MPRA_paper_92247.pdf
    File Function: original version
    Download Restriction: no
    File URL: https://mpra.ub.uni-muenchen.de/92326/1/MPRA_paper_92326.pdf
    File Function: revised version
    Download Restriction: no
    File URL: https://mpra.ub.uni-muenchen.de/109330/1/MPRA_paper_92326.pdf
    File Function: revised version
    Download Restriction: no
    ---><---

    References listed on IDEAS

    as
    1. Billot, Antoine & Thisse, Jacques-Francois, 2005. "How to share when context matters: The Mobius value as a generalized solution for cooperative games," Journal of Mathematical Economics, Elsevier, vol. 41(8), pages 1007-1029, December.
    2. Béal, Sylvain & Ferrières, Sylvain & Rémila, Eric & Solal, Philippe, 2018. "The proportional Shapley value and applications," Games and Economic Behavior, Elsevier, vol. 108(C), pages 93-112.
    3. Casajus, André, 2018. "Symmetry, mutual dependence, and the weighted Shapley values," Journal of Economic Theory, Elsevier, vol. 178(C), pages 105-123.
    4. Manfred Besner, 2019. "Axiomatizations of the proportional Shapley value," Theory and Decision, Springer, vol. 86(2), pages 161-183, March.
    5. Barry Feldman, 2000. "The Proportional Value of a Cooperative Game," Econometric Society World Congress 2000 Contributed Papers 1140, Econometric Society.
    6. René Brink & Gerard Laan & Valeri Vasil’ev, 2014. "Constrained core solutions for totally positive games with ordered players," International Journal of Game Theory, Springer;Game Theory Society, vol. 43(2), pages 351-368, May.
    7. Jean Derks & Hans Haller & Hans Peters, 2000. "The selectope for cooperative games," International Journal of Game Theory, Springer;Game Theory Society, vol. 29(1), pages 23-38.
    8. K. Michael Ortmann, 2000. "The proportional value for positive cooperative games," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 51(2), pages 235-248, April.
    9. Hart, Sergiu & Mas-Colell, Andreu, 1989. "Potential, Value, and Consistency," Econometrica, Econometric Society, vol. 57(3), pages 589-614, May.
    10. Gangolly, Js, 1981. "On Joint Cost Allocation - Independent Cost Proportional Scheme (Icps) And Its Properties," Journal of Accounting Research, Wiley Blackwell, vol. 19(2), pages 299-312.
    11. René Brink & René Levínský & Miroslav Zelený, 2015. "On proper Shapley values for monotone TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 449-471, May.
    Full references (including those not matched with items on IDEAS)

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. 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.
    2. Manfred Besner, 2019. "Axiomatizations of the proportional Shapley value," Theory and Decision, Springer, vol. 86(2), pages 161-183, March.
    3. 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.
    4. Besner, Manfred, 2021. "Disjointly and jointly productive players and the Shapley value," MPRA Paper 108511, 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. Besner, Manfred, 2017. "Axiomatizations of the proportional Shapley value," MPRA Paper 82990, University Library of Munich, Germany.
    7. Besner, Manfred, 2017. "Weighted Shapley levels values," MPRA Paper 82978, University Library of Munich, Germany.
    8. Besner, Manfred, 2022. "The grand surplus value and repeated cooperative cross-games with coalitional collaboration," Journal of Mathematical Economics, Elsevier, vol. 102(C).
    9. Wenzhong Li & Genjiu Xu & Hao Sun, 2020. "Maximizing the Minimal Satisfaction—Characterizations of Two Proportional Values," Mathematics, MDPI, vol. 8(7), pages 1-17, July.
    10. Manfred Besner, 2020. "Parallel axiomatizations of weighted and multiweighted Shapley values, random order values, and the Harsanyi set," Social Choice and Welfare, Springer;The Society for Social Choice and Welfare, vol. 55(1), pages 193-212, June.
    11. Béal, Sylvain & Ferrières, Sylvain & Rémila, Eric & Solal, Philippe, 2018. "The proportional Shapley value and applications," Games and Economic Behavior, Elsevier, vol. 108(C), pages 93-112.
    12. Besner, Manfred, 2021. "Disjointly productive players and the Shapley value," MPRA Paper 108241, University Library of Munich, Germany.
    13. René Brink & René Levínský & Miroslav Zelený, 2015. "On proper Shapley values for monotone TU-games," International Journal of Game Theory, Springer;Game Theory Society, vol. 44(2), pages 449-471, May.
    14. Zhengxing Zou & Rene van den Brink, 2020. "Sharing the Surplus and Proportional Values," Tinbergen Institute Discussion Papers 20-014/II, Tinbergen Institute.
    15. Pierre Dehez, 2017. "On Harsanyi Dividends and Asymmetric Values," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 19(03), pages 1-36, September.
    16. Besner, Manfred, 2021. "The grand dividends value," MPRA Paper 107615, University Library of Munich, Germany.
    17. Besner, Manfred, 2021. "The grand dividends value," MPRA Paper 106638, University Library of Munich, Germany.
    18. Besner, Manfred, 2018. "Player splitting, players merging, the Shapley set value and the Harsanyi set value," MPRA Paper 87125, University Library of Munich, Germany.
    19. Demuynck, Thomas & Rock, Bram De & Ginsburgh, Victor, 2016. "The transfer paradox in welfare space," Journal of Mathematical Economics, Elsevier, vol. 62(C), pages 1-4.
    20. 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).

    More about this item

    Keywords

    TU-game · Value dividends · (Generalized) Harsanyi set · Weighted Shapley values · (Proportional) Harsanyi payoff · Sharing function systems;

    JEL classification:

    • C7 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory
    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:pra:mprapa:92247. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Joachim Winter (email available below). General contact details of provider: https://edirc.repec.org/data/vfmunde.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.