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On Harsanyi dividends and asymmetric values

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  • Pierre Dehez

Abstract

The concept of dividend in transferable utility games was introduced by Harsanyi [1959], offering a unifying framework for studying various valuation concepts, from the Shapley value to the different notions of values introduced by Weber. Using the decomposition of the characteristic function used by Shapley to prove uniqueness of his value, the idea of Harsanyi was to associate to each coalition a dividend to be distributed among its members to define an allocation. Many authors have contributed to that question. We offer a synthesis of their work, with a particular attention to restrictions on dividend distributions, starting with the seminal contributions of Vasil’ev, Hammer, Peled and Sorensen and Derks, Haller and Peters, until the recent papers of van den Brink, van der Laan and Vasil’ev.
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  • Pierre Dehez, 2017. "On Harsanyi dividends and asymmetric values," LIDAM Reprints CORE 2902, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
    • Handle: RePEc:cor:louvrp:2902
    Note: In : International Game Theory Review, 19(3), 2017
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    Cited by:

    1. Pierre Dehez & Victor Ginsburgh, 2020. "Approval voting and Shapley ranking," Public Choice, Springer, vol. 184(3), pages 415-428, September.
    2. Dehez, Pierre, 2023. "Sharing a collective probability of success," Mathematical Social Sciences, Elsevier, vol. 123(C), pages 122-127.
    3. Pierre Dehez, 2024. "Cooperative Product Games," International Game Theory Review (IGTR), World Scientific Publishing Co. Pte. Ltd., vol. 26(01), pages 1-13, March.
    4. Manfred Besner, 2022. "Harsanyi support levels solutions," Theory and Decision, Springer, vol. 93(1), pages 105-130, July.
    5. Estela Sánchez-Rodríguez & Miguel Ángel Mirás Calvo & Carmen Quinteiro Sandomingo & Iago Núñez Lugilde, 2024. "Coalition-weighted Shapley values," International Journal of Game Theory, Springer;Game Theory Society, vol. 53(2), pages 547-577, June.

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    JEL classification:

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

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